CRYSTALLOGRAPHY.(1934-1935.)CRYSTAL PHYSICS.The Electron Theory of Metals.--Tt has long been known that thecharacteristic structure of certain alloys is determined not so muchby its composition as by the ratio of the total number of valencyelectrons t o the total number of atoms in the unit cell. Thus, thecharacteristic complex structure of y-brass is shared by the alloysCu5Zn8, Cug& Cu,Sn8, Ni5Zn21, and many others which all have incommon an electron : atom ratio of 21. : 13. Similarly, the structureof p-brass corresponds to an electron : atom ratio of 3 : 2, and thatof &-brass to a ratio of 7 : 4. These ratios, first put forward onempirical grounds by Hume-Rothery in 1927, have recently beengiven a quantum-mechanical explanation by H. J0nes.l An attemptis here made to give an elementary physical picture which willconvey the essential features of the theory.The state of an electron may be completely defined in terms ofthe three co-ordinates kz, E,, and E, of its momentum.If weimagine these co-ordinates to be plotted along three rectangularaxes, the state of the electron is described by the point (kx, k,, kz)in the momentum space thus defined. If the electron is free, theenergy associated with the state is proportional to the square ofthe momentum, i e . , to the square of the vector joining the point inquestion to the origin of momentum space. On account of thequantum conditions and the exclusion principle, no two electronsmay exist in the same state, so that each electron requires foritself a definite volume of momentum space, and an assemblage ofmany electrons will occupy a spherical domain whose size is deter-mined by the number of electrons considered.If the electrons arenot free, as will be the case in a crystal where we must take intoaccount the effect of the lattice field, it can be shown that the energyof the electron no longer varies continuously with the momentum,but that there are certain planes in momentum space such thatwhen the point describing the state of the electron crosses one ofthese planes a discontinuous energy change takes place.2 Theelectrons in the neighbourhood of a discontinuity are those whose1 Proc. Roy. Soc., 1934, [A], 144, 225 ; A., 1934, 483.2 Brillouin, “ Quantenstatktik,” Chap.8; A. Sommerfeld and H. A.Bethe, “ Handbuch der Physik,” XXIV, 2182 CRYSTALLOGRAPHY.wave-length and direction would lead them to be reflected by thecorresponding plane of the crystal. Just below the plane theenergy is abnormally depressed ; just above ib, abnormally raised.Between successive planes the energy varies continuously withmomentum and approximates to that of a free electron, It niaybe shown, further, that the planes in momentum space acrosswhich these energy discontinuities take place are parallel to allpossible crystallographic planes in the crystal, so that in the case ofe.g., a cubic substance, the origin is surrounded by a series ofconcentric zones successively bounded by the faces 01 the cube, thedodecahedron, the octahedron, and so on.The magnitude of theenergy jump across the various zones is not constant, but is pro-portional to the degree of scattering of electron waves from thecorresponding plane in the crystal, and therefore closely relatedto the intensity of the X-ray reflexion : if all the atoms in thestructure have nearly the same atomic number, it is actuallyproportional to the amplitude of this reflexion.In the y-alloys, experiment shows that, of the planes with smallindices, only those of the forms (411) and (330) give rise t o strongX-ray reflexion. We therefore conclude that the first planes inmomentum space outwards from the origin across which the energyshows an appreciable discontinuity are those lying parallel t o facesof these two forms.The figure bounded by these two forms is apolyhedron of 36 faces, not very far from spherical in shape.Let us now imagine that the number of electrons in the structureis gradually increased from zero. At first, the Fermi distribution,i.e., the volume occupied by the states oi the electrons in momentumspace, will grow very nearly spherically until it comes into proximitywith the faces of the zonal polyhedron. When the sphere touchesthe zone, the distribution will no longer grow in that particulardirection, since to do so would correspond to a large energy incre-ment, but rather in other directions in which growth can still takeplace without the zone being crossed. The distribution will there-fore ultimately assume a distorted shape approximating to that ofthe zone. Jones has calculated that in the case of the y-alloys, fora unit cell containing 62 atoms, the spherical Fermi distributioninscribed in the zoiial polyhedron corresponds to 80 electrons,whereas the whole polyhedron would hold 90.The actual numberof electrons in the unit cell is 84, so that in the y-alloys the surfaceof the Fermi distribution lies very close to the surface of energydiscontinuity. This Jones states to be the distinguishing featureof the ?-structures. The exact filling of the zone corresponds tolowering of the energy of the lattice relative to other lattices with adifferent zone arrangement, and consequently adds stability to thBERNAL : CRYSTAL PHYSICS. 183structure. In terms of the theory of diamagnetic susceptibilitygiven by R. Peierls,3 it accounts for the remarkably large diarnagneticsusceptibilities of the y-alloys, and it also gives an explanation ofthe large Hall coefficient which tliese alloys show.H.Jones4 has now extended the theory to the case of E- andq-phases, and has succeeded in accounting for the observed variationof the axial ratio with composition in these phases and also for therange of composition over which the phase is stable. In thesecases, and also in the case of bismuth, there is a very small butfinite ‘ overlap ’ of the Fermi distribution beyond the first Brillouinzone. From this, the diamagnetic susceptibilities of bismuth andsome of its alloys, and also the magnetostriction, are deduced ingood agreement with experiment.The application of the theory t o the p-phase has been consideredby U.Dehlinger,5 who shows that in this case the first zone is onlypartially filled, since the number of electrons which it would accom-modate is two per atom whereas the observed electron : atomratio is 3 : 2. This, according t o Dehlinger, corresponds to thefact that p-phases are stable only at high temperatures.As the result of these theoretical advances, we are now in a,position t o get a general view of metal chemistry and its relationto the other parts of chemistry. Such a picture has been givenby F. Hund.6 In it, electrons are pictured as occupying bondingand anti-bonding states. If each atom brings so few electrons thatonly part of the former are filled, the result is a metal of the generalA type of alkalis and alkaline earths.When the bonding zone isexactly filled, the result is an insulator of the type of diamond.If part of the next anti-bonding zone is filled, the result will beagain a metal, but of the B type of bismuth or tellurium (theelectrons of course can be used to form a closed shell molecule asin red selenium, Ses, or yellow phosphorus, P4). Finally, if bothzones are filled, the result is again an insulator, this time a rare gas.E. Wignerand F. Seitz 7 and J. C. Slater 8 have calculated the energies andlattice constants of sodium and lithium on the basis of free electronbinding.With the adamantine class and the B-group metals, it isimpossible to go so far. Clearly, here a considerable part of thelattice energy is derived from the degree of filling of the BrillouinThe theory of the A type metals is fairly satisfactory.2.Physik, 1933, 80, 763.4 Proc. Roy. Soc., 1934, [A], 147, 396; A., 1935, 153.5 %. Phystk, 1935, 94, 231 ; Metallwirt., 1935, 14, 145.7 Physical Rev., 1933,43,804; 1934,46,509, 1102; 1935,47,400.* Ibid., 1934, 45, 794; Rev. Mod. Physics, 1934, 6, 209.‘‘ The Solid State of Matter,” Phys. SOC, Rep., 1935, p. 36184 CRYSTALLOGRAPHY.zones as in the Jones theory. The corresponding calculatioiishave been done for the diamond 9 with qualitatively satisfactoryresults, although no theory has its yet served to explain the veryremarkable optical and photoelectric properties of diamonds which,as (Sir) R.Robertson, J. J. Pox, and A. E. Martin lo have shown,differentiate them into two widely different types.The adamantine compounds can, however, also be formulated asmacro-molecules with shared electron orbitals. They mark theboundary between the explanation of crystal structures by metallicor by homopolar conceptions.The structure of the transition metals offers more theoreticaldifficulties because here the core as well as the free electrons has tobe taken into account. K. Fuchs l1 has calculated the equilibriumcopper lattice with fair success.The magnetic and electrical properties of the transition metalsand of some of their alloys, particularly those of nickel, have beendiscussed from a somewhat different point of view by N. F.Mott.12In the case of the transition metals partially filled d levels exist, andthe extra electrons contributed by other atoms in the alloy can goto fill up these levels. U. Dehlinger 13 from structure considerationsconcludes that all the transition metals except iron contain onlyone s electron. We are, however, far from having as yet an adequatetheory of the transition metals.Order-Disorder Transformations in Alloys.-Where two metalsare alloyed together, a series of solid phases is in general formed.The composition of each phase can be varied continuously over acertain range, within which the alloy remains homogeneous, andwhich generally includes a composition of relatively simple atomicproportions. We may therefore regard each phase as having someideal composition, departures from which can take place withoutthe appearance of a new phase by the statistical replacement ofsome atoms of one constituent by atoms of the other.Thus, totake a concrete example, in the system Au-Cu two of the phaseshave the ideal compositions CuAu and Cu,Au. When we investigatethe structure of such a phase, we find in general that in a properlyannealed specimen the two types of atom assume definite relativepositions in the structure. In the phase Cu,Au, the gold atoms arefound at the corners of a simple cubic unit cell, the copper atomsoccupying the centres of the faces. Such a structure is termed aW. F. Laschkarev and A. 8. Tschabau, Physikal. 2. Sovietunion, 1935, 8,240 ; Kimball, J . Chem. Physics, 1935, 3, 560 ; Nath, Proc.Indian Acad. Sci.,1934,1, [A], 333; 1935,1, [A], 841; 2, [A], 143.lo Phil. Trans., 1934, [ A ] , 232, 463.l1 Proc. Roy. Soc., 1935, [A], 151, 585.l2 Proc. Physical SOC., 1935, 47, 571. l3 2. Physik, 1935, 96, 620BERNAL : CRYSTAL PRYSICS. 185' super-lattice.' If, however, the alloy is not annealed but quenchedfrom a sufficiently high temperature, we find that, while preciselythe same sites are occupied by atoms as in the super-lattice, thedistribution of the two metals between them is no longer regularbut purely random. Thus, in the example we have quoted, thestructure becomes essentially a face-centred cubic one, with a unitcell of the same size as before, but in which each site is occupied by($Cu + ~ A u ) .The transition between the ordered distribution in the super-lattice and the corresponding disordered arrangement has been thesubject of much recent work.14 All the authors agree in treatingit essentially as a problem of dynamic equilibrium in which the atomsseek to take up the ordered arrangement of lowest potential energy,while thermal agitation seeks to promote a state of disorder.Herewe shall follow in the main the discussion of W. L. Bragg andE. J. Williams, for although it cannot claim to be the earliest treat-ment of the order-disorder transformation, yet it contains manynovel features and has the additional advantage of being mathe-matically less formal than that of the other authors, and therefore,perhaps, more suitable for this Report.Consider a structure in a, condition intermediate between theextreme ordered and disordered states.Its state may be representedby a quantity X, the degree of order, whose value is unity for theordered arrangement of the super-lattice and zero for the state ofcomplete disorder. (The exact definition of X is irrelevant for ourdiscussion, and in fact, the quantity is differently defined by theseveral authors.) For a given value of 8, and a t a given temper-ature T, we may then define a quantity V as the increase in potentialenergy of the crystal when one atom is moved from an ordered to adisordered position. This quantity V is not a constant but afunction of X, for when X = 0 the distinction between ordered anddisordered positions vanishes and V must be zero; V will rise to amaximum value V,, when X = 1.As a first approximation, V isassumed to be proportional to X and to vary only slowly with T.The general form of the variation of V as a function of 8 at severaldifferent temperatures is shown by the curves of Pig. lb.If, now, we consider the crystal a t a temperature T, the conditionthat a degree of order X is one of dynamical equilibrium at thatl4 W. Gorsky, 2. Physik, 1928, 50, G4; U. Dehlinger, ibid., 1933,83, 832,and earlier papers; 2. physikal. Chew&., 1934, [B], 26, 343; A., 1934, 724;G. Borelius, Ann. Physilc, 1934, 20, 57, 650; A., 1934, 724; 1935, 24, 489;W. L. Bragg and E. J. Williams, Proo. Roy. rs(oc., 1934, [A], 145, 699; A.,1934, 954; 1935, [A], 151, 540; H.A. Bethe, ibid., 150, 552; A., 1193; W.Kume-Rothery and H. M. Powell, 2. Krist., 1935,91,23186 CBYSTAILOUItAPIIY.temperature leads to an expression for 8 as a function of V and 2'.Here we shall expect the form of the relation to be more exactlydetermined, for on the assumption of thermal equilibrium, thedistribution of atoms as between the ordered and the disorderedposition will be given by the Boltzinann relation as a function ofVIET. Without entering into details, we may say that Bragg andWilliams show that the general form of the relation will be thatshown by the curves of Fig. la. At low temperatures, or for largevalues of V , the degree of order approaches unity, while for smallvalues of V or under conditions of extreme thermal agitation, thedegree of order is very small.The equilibrium degree of order atany temperature T is given by the intersection of the two corre-sponding curvcs of Fig. 1. At high temperatures the only iiiter-section is a t 0, corresponding to complete disorder. At low temper-atures it is easy to see that the intersection at 0 corresponds to anunstable equilibrium, and that a second intersection a t a finite valueof S represents the stable equilibrium. This value of S tends tounity as T approaches zero. This second intersection will onlyoccur below a certain critical temperature T,, and from the natureof the curves it is clear that the point of intersection varies veryrapidly as T falls below this critical temperature. On cooling, thereis therefore a sudden onset of order below T,, followed by a moregradual increase towards unity.Formally, the theory of order-disorder is closely analogous t othat of ferromagnetism, the ordered form corresponding to theferromagnetic, and the disordered to the paramagnetic state ;T, corresponds to the Curie point.The existence of this critical temperature is the most importantfeature of the theory, for it is to be expected that at this temperaturemany of the physical properties of the alloy will display sharpchanges.In particular, anomalies in the specific heat will bBERNAL : CRYSTAL PHYSICS. 187expected, for as the temperature of the alloy is raised, extra thermalenergy must be supplied to break down the ordered structure of thecrystal.The specific heat will, therefore, rise gradually to thecritical temperature and then, all order being destroyed, fall abruptlyto its normal value. Bethe, who discusses the question of specificheats in rather more detail, shows that, although the order asdefined by Bragg and Williams disappears at the temperature T,,there is still a measure of ‘ local order ’ which persists above thistemperature and contributes to the energy of the structure. AboveT,, therefore, the specific heat of the alloy is still somewhat largerthan its normal value. In this iorm, the theory is in very satis-factory agreement with the specific-heat measurements of C. Sykes 15on the alloy CuZn.A somewhat different type of transformation between the orderedand disordered states takes place when the curves of Fig.la have apoint of inflexion, being curved to the x axis in the neighbourhoodof the origin. This will be the case, as Bragg and Williams show,for the alloy Aldu. Now, there will no longer be a continuous,albeit rapid, decrease of S as the temperature reaches T,, for therewill be a certain temperature a t which the curve of Fig. l b will betangential to that of Fig. l a , not at the origin but at some pointcorresponding to a finite value of 8. Above this temperature, thecurves will not intersect at all and the degree of order will fallabruptly to zero. In this case, the energy change associated with thetransformation must be regarded as a latent heat of transformationrather than as an anomalously high specific heat.Here again, thetheory is in satisfactory agreement with Sykes’s measurementson Cu,Au.In both cases the development of the ordered from the disorderedphase is a process which depends on the rate of cooling. At anygiven temperature below T, there is a definite rate a t which theorder increases. Bragg and Williams have shown that a time ofrelaxation T exists, after which the departure from equilibriumreaches 1 / e of iLs original value T, and which is given by e-logA(F1’T-l),where A = 10-12 sec. and TI is the temperature for which thetime of relaxation is I sec. If TIT, is 8, z is 30,000 years, so thatthe alloy will never in practice reach order at temperatures lessthan +Tl. This fixes another characteristic temperature, theimportance of which is that no ordered state for which T, < +TIcan ever be formed by cooling.This is the probable reason whysuperstructures other than very simple ones do not appear.The theory of order and disorder in crystal structures has beenstudied chiefly in metals, but :malogous phenomena are being15 Proc. Roy. Roc., 1935, [A], 148,422188 CRYSTALLOGRAPHY.observed with increasing frequency with other compounds, particu-larly among mixed oxides, sulphides, and halides. The interstitialand subtraction " Berthollide " compounds l 6 have, in general,atoms which occupy a larger number of lattice points, either regularly(ordered) or statistically (disordered). These compounds havebeen discussed by E. J. W. Verwey 17 and G. Htigg.l* Of particularinterest is the compound Ag,HgI, which exists in two forms-atetragonal form with definite positions of the metal atoms, and ahigher-temperature cubic form in which the metal atoms occupystatistically three out of the four octahedral positions.A moreextreme case is provided by the high-temperature form of silveriodideJ20 where the silver atoms occupy one of the three possibleoctahedral holes of the body-centred iodine lattice.Further examples of this phenomenon are (Li1Ti4+)0 2l withan NaCl lattice, Ce2,,W0, 22 isomorphous with CaWO,, the tungstenbronzes Na,W0,,23 in which the WO, lattice takes up Na atoms bylowering the tungsten valency, and the heteropoly-acids.24This phenomenon is closely related to the polysynthetic twinningwhich is being found very frequently in layer and chain lattices.Cadmium bromide,25 for instance, occurs in a cell containing one-third of a molecule due to existence of alternate layers of CdC1,and CdI, structures.Pd(NH,),C12,26 AgCN,27 and cristobalite 28show analogous two-dimensional lattices. Disordered and statisticalphenomena in crystals are, indeed, generally to be expected wheneve;.different structural arrangements exist having approximately thesame energy.Formally analogous to the order-disorder phenomenon is that ofthe rotation of molecules in crystals.29 The general theory hasnow been given by R. H. F0wler.3~ Two kinds of change occur, ingeneral. In the first, the inception of rotation coincides with ttchange of crystal structure and there is a definite latent heat.l6 See Ann.Reports, 1933, 30, 381.Is J. A. A. Ketelaar, ibid., 1934, 87, 436; A., 1934, 947; 2. physikal.2o L. W. Strock, 2. physikal. Chem., 1934, [B], 25,441; A., 1934, 834.21 E. Kordes, 2. Krist., 1935, 91, 193; 92, 139.23 J. Beintema, Proc. K. Akad. Wetensch. Amsterdam, 1935, 38, 1011.23 G. Hiigg, 2. physikal. Chem., 1935, [El, 29, 192; Nature, 1935, 135, 874.24 See ref. (97), p. 220.26 F. G. Manii, (Miss) D. Crowfoot, D. C. Gattiker, and (Mrs.) N. Wooster,2 7 C. D. West, 2. Krist., 1935, 90, 555; A., 1194; 1934, 88, 173.2 8 W. Nieuwenkamp, ibid., 1935, 90, 377.29 See Ann. Reports, 1931, 28, 290.30 Proc. Roy. SOC., 1935, [A], 151, 1; A,, 1197.17 J . Chem. Physics, 1935, 3, 592.2. Krist., 1935, 91, 114.Chem., 1934, [B], 26,327; 1935,30,53.26 See ref.(94), p. 209.J., 1935, 1642BERNAL : THE PROPERTIES OF REAL CRYSTALS. 189In the second, the inception of rotation is gradual, but it becomescomplete at a definite temperature : there is no latent heat but ananomalous rise in the specific heat. In general, these first andsecond types of change occur in different substances, but B. Ruhe-mann has shown that both occur in ammonium chloride, the firstat high the second at low pressures. L. Landau31 has given thetheory of this change-over, and has shown that a critical pressuremust exist at which the two types coincide. The theory cannot begiven here, but it expresses the fact that an increase of interactionbetween the movable parts beyond a certain degree causes all tomove when one does, and therefore a change from the second to thefirst type of transformation.J. D. B.THE PROPERTIES OF REAL CRYSTALS.The mechanical properties of real crystals, in so far as they departfrom those to be expected in a crystal having an ideal structure,were discussed in the last Report on Crystallography. During theperiod under review, however, the nature of the real crystal has beenthe subject of so many publications that no excuse is offered foronce again discussing this subject. Apart from individual papers,two especially important publications may be mentioned : vix.,the Report of the International Conference on Physics on theSolid State of Matter and an issue of the Zeitschrift fur Kristal-Eographie devoted entirely to the real crystal.Secondary Structure.-The conception of a crystal as having ablock-like structure was originally advanced to explain the fact thatthe observed X-ray reflexions from a crystal are very much moreintense and extend over a much wider angle than is to be expectedfrom an ideal structure.This conception has since been appliedin an attempt to explain many other ' structure-sensitive ' properties,notably breaking strength, which cannot be satisfactorily accountedfor in terms of the ideal lattice. The exact nature of this secondarystructure, and even its very existence, is still, however, the subjectof violent controversy. Thus, while many results are interpretedin terms of such a structure, and others 3 are alleged to give directproof of its existence, other authors 4 have marshalled many factswhich they claim render such a structure impossible, and at theThe Physical Society, London, 1935 ; hereafter referred to as Phycl.SOC.31 Physikal. 2. Sovietunion, 1935, 0, 113.Rep.1934,89, 193-415.3 F. Bitter, Physical Rev., 1932, 40, 125; A., 1933, 1234.H. E. Buckley, 2. Krist., 1934,89,221,410; A., 1935, 150; M. J. Buerger,ibid., p. 242190 CRYSTaLLOQEAPHY.same time criticise the evidence on which the secondary structureis based. Among the principal objections to a mosaic structure ofthe type postulated by Zwicky are: (1) The fact that coherentcrystals can be grown 8,s thin plates or hairs with linear dimensionsless than those of the mosaic blocks.(2) The internal perfectionof crystals which makes their use in optical systems possible.(3) Intersecting glide planes. Gliding is supposed to take place onso-called x-planes : gliding on two intersecting n-planes couldonly occur if the glide distance was an exact multiple of the n-planespacing. (4) Crystal strength. The very low strength of crystals,compared with the value calculated from the ideal structure, doesnot require any secondary structure and can be explained as due toa tearing of the crystal starting from surface cracks.5 A. Joff66has shown that under appropriate conditions strength approximatingto the theoretical can be achieved, while with glass, where there isno question of mosaic structure, the abnormally low strengthobserved can be attributed to tearing.Mica stretched in such away that the edges remain stressless increases in strength ten times.( 5 ) The energetics of the problem.’A number of interesting observations have been explained byA. Goetz 8 in terms of a ‘ group ’ structure, but here again there aremany object ions. 9Another type of secondary structure, which seems to be lessopen to criticism, is the ‘lineage structure’ of M. J. Buerger.10Mere all crystals are regarded as essentially filled in dendriticframeworks. The lack of perfect parallelism between lineagesaccounts for the observed decrease in X-ray extinction, but thestructure is essentially not a mosaic one. It is only accurate toapply the term mosaic to one cross section of the crystal, for inthree dimensions the mosaic ‘ blocks ’ join one and the same parentstock at the original crystal nucleus.The ‘ blocks ’ are lineagesjust as are the branches of a dendrite. Buerger supports his viewsby a number of beautiful photographs, and is able to account in ageneral way for most of the structure-sensitive properties normallyexplained in terms of a secondary structure. In this connectionwe may refer the reader t o the work of A. Papapetrou l1 on the growthof dendritic crystals.On the experimental side, the extreme difficulty of obtainingreproducible results, and the amazing discrepancies between theE. Orowan, Phys. SOC. Rep., p. 81; 2. h7rist., 1934, 89, 327; A., 1935, 151.cI Phys. SOC. Rep., p. 77.7 M. J. Buerger, 2.Krist., 1934,89, 242; E. Orowan, Phys. SOC. Rep., p. S1.* 2. Krist., 1034, 89, 310; A., 1935, 151; Phys. SOC. Rep., p. 62.H. E. Buckley, 2. Krist., 1934, 89, 221; A., 1935, 150.l1 Ibid., 1935, 92, 89. 50 ITbid., p. 195BERNAL: THE PROPERTIES OF REAL CRYSTALS. 191observations of different schools, make it difficult to establish anyunquestionable conclusions, To instance only one example, allauthors are agreed that wetting a rock salt crystal has a profoundeffect on its plastic properties and breaking strength. K. Wenden-burg l2 argues that the effect is st volume one due to penetration ofthe water into the crystal, since the effect persists if the surface issubsequently dried. Absorption spectra are also said to revealthe presence of water in the crystal.A. J0ff6,13 however, claims thatthe effect cannot be a volume one since the strength of a wettedcrystal, one region on the surface of which is protected by vaselin,is that of a dry crystal. If water entered the volume of the crystalit would penetrate to all parts in spite of the vaselin.That a secondary structure is not an essential characteristic ofcrystal is indicated by the fact that crystals of rock salt can beprepared l* which give the X-ray reflexion deduced from the ideallattice. A summary of existing theories of real crystals is givenby A. Smekal.l5Plasticity.-Closely allied to the question of secondary structureis that of the plastic properties of single crystals. In the " Distor-tion of Metal Crystals " 16 and elsewhere,l' accounts are availableof the many observations on plastiic deformation. The essentialfeatures which any theory of plasticity must explain are : (1) Plasticdistortion sets in when the shear stress reaches a certain criticalbut very small value.(2) The distortion may take place eitherby gliding along definite crystallographic planes in, definite directions,or by twinning. (3) The occurrence of plastic deformation isalways accompanied by a ' hardening ' or increase in 'the stressrequired to produce further deformation. In this connexion, it isimportant to realise, as A. W. Stepanow has pointed out, thatbreaking strength and plasticity are in no way related, and that noincrease in breaking strength takes place on plastic deformation.The anomalously low breaking strength, as we have seen, is to findits explanation in the secondary structure : it can only be measuredunder conditions in which plastic flow is prevented.12 2.Krist., 1934,88, 727; A., 1934, 721.13 Phys. SOC. Rep., p. 72; see also E. W. Zehnowitzer, Nature, 1935, 135,1076; A., 956.14 M. Renniger, Naturwiss., 1934, 22, 334; A., 1934, 720; 2. Krist., 1934,89, 344; A., 1935, 151 ; P. P. Ewald and M. Renniger, Phys. SOC. Rep., p. 57.15 2. Krist., 1934, 89, 386; A., 1935, 161.16 (Miss) C. F. Elam (Oxford, Clarendoir Press, 1935).17 W. G. Burgers, Phys. SOC. Rep., p. 139; E. Schmid, ibid., p. 161; W. G.Burgers and J. M. Burgers, First Report on Viscosity and Plasticity, Verh.K. Akad. Amsterdam, 1935,15,173.18 2.Physik, 1934, 94, 42192 CRYSTALLOGRAPHY.The same author l9 has suggested that plasticity may be accountedfor in terms of the intense local heating developed in the neighbour-hood of the glide planes, which produces a temporary dissociationof the lattice. That such a mechanism is not impossible is indicatedby the experiments of F. P. Bowden and K. E. W. Ridler,20 whofound that the surface temperature of sliding metals may reachvery high values although the bulk of the metal remains at roomtemperatures. High temperatures produced by plastic deformationmay play an important part in detonation.21 The great plasticityof silver chloride compared with that of rock salt, which has the samestructure and very nearly the same lattice dimensions and latticeenergy, suggests that the difference may be due to the differenceof polarisation properties of sodium and silver, which also accountsfor the absence of cleavage in silver chloride.22A more precise, mathematical theory of the plasticity of crystalshas been developed by G.I. Taylor,23 who pictures slip as takingplace by the propagation of a ' dislocation ' along the slip plane.Such a ' dislocation ' may be pictured by considering a point P inthe slip plane, such that some distance beyond P the lattice iscontinuous across this plane, while at some distance on the otherside of P the lattice is again continuous but with the portion on oneside of the slip plane displaced relative to that on the other throughthe length of the unit cell.In the immediate neighbourhood of P ,.the lattice is distorted, but where P has passed along the slip planethe ideal lattice is restored except that one half is displaced relativeto the other. To bring about such a displacement by causing allthe atoms in one plane to jump simultaneously through the lengthof one unit cell would require a force of the order of magnitude of theelastic modulus, but if the displacement occurs by the atoms in theneighbourhood of the dislocation jumping one by one, therebypropagating the dislocation, the force required is much smaller,since the field of force in the immediate neighbourhood of the dis-location is profoundly altered. Calculation shows, in fact, that underthe influence of the smallest stress, thermal agitation alone shouldsuffice to propagate the dislocation, so that an ideal lattice shouldbe infinitely weak.Taylor overcomes this objection by supposingthat, after travelling a distance L, the dislocation encounters oneof the ' faults ' of the secondary structure and then stops. In thisIs 2. Physik, 1933, 81, 560.20 Proc. Cam&. Phil. Xoc., 1935, 31, 431.21 A. Michel-L6vy and H. Muraour, Compt. rend., 1934,198,1499; A., 1934,22 A. W . Stepanow, Physikal. 2. Sovietunion, 1934, 6, 312 ; 1935, 8, 25.23 Proc. Roy. SOC., 1934, [A], 145, 362, 357; A., 1934, 950; 2. Krist., 1934,605.89, 376; A., 1935, 151EVANS : CRYSTALLOURAPHY. 193way a parabolic relation is derived between the stress and the amountof plastic distortion, which is in good agreement with observationson rock salt and metal crystals.The experiments enable a value ofL of about 10-4 cm. t o be deduced, and this is of the correct order ofmagnitude for most of the theories of secondary structure.Another picture of the mechanism of plastic deformation, due toE. Orowan,24 regards it as essentially a dynamic phenomenon.Consider a crystal under the influence of a shearing stress T,, itselfinsufficient to cause gliding. Under the influence of local thermalfluctuations, the stress will occasionally reach a value exceedingsome critical value TR and local slip will take place. This is mostlikely to happen at places where the stress is already concentratedowing to material inhomogeneities, so that we must replace the meanstress 7, by cpa, where q is a factor expressing the local concentrationof stress.The increase of stress from qz, to TR corresponds to anincrease of elastic energy proportional to (TR - q ~ # , and it istherefore assumed that the probability of such an occurrence isgiven by the Boltzman equation W = const. x e - h - P Q l k T . Thevelocity of the deformation process is evidently proportional to thisprobability. In this form, the theory gives a finite rate of deform-ation for all values of the applied stress. The exponential factor,however, results in such a rapid increase in velocity with appliedstress that there will be some critical stress below which the velocityis too small to be observed, as is found to be the case experimentally.Orowan’s theory gives a satisfactory account of the parabolicrelationship between stress and amount of deformation, and also ofthe observed temperature variation of critical stress.A suggestedcombination of the theories of Taylor and Orowan has been advancedby Burgers and Burgers.25 J. D. B.CRYSTALLOGRAPHY.The Technique of Structure Analysis.-The field of X-ray structureanalysis has enjoyed two important additions to its bibliographyduring the period under review. ‘‘ International Tables for CrystalStructure Determination ” is the outcome of the work of an inter-national committee of crystallographers set up 1929,2 and containsa wealth of information for those engaged on structure analysis.The first volume comprises diagrams of the equivalent generalposition in the 230 space groups, together with the structure factorsand a list of the characteristic reflexions both for the general and24 2.Physik, 1934, 89, 605, 614, 634; 1935,97,673.25 Op. cit., ref. (17).2 See Ann. Reports, 1931, 28, 263.1 Bell, 1935 (two vols.).REP .-voL. XXXII. 194 CRY STALLOGRAPHY.for special positions in each space group. The second volumecontains tables of many trigonometrical functions and physicalquantities frequently required in structural analysis, as well as anaccount of graphical methods of interpreting X-ray photographs." X-Rays in Theory and Experiment," 3 a second and greatlyenlarged edition of " X-Rays and Electrons," contains some 150pages devoted to a very full account of the theory of the diffractionof X-rays by a crystal grating, much of which was previouslyunavailable in the English language outside original papers.The experimental methods of structure analysis have suffered nofundamental changes in the last two years.Two papers,4 dealingwith the Weissenberg camera and with the interpretation of thephotographs obtained, reflect the increasing use which is being madeof this instrument. Photographic methods of intensity measure-ment have now become a common practice. I n a moving-filmcamera described by J. M. Robertson,s the crystal under investi-gation and a standard crystal are alternately exposed to the X-raybeam so that a number of reflexions of known intensity are presenton the film: by comparison with these reflexions, unknown intensitiescan be determined with an accuracy amply sufficient for structureanalysis in a fraction of the time required for ionisation-spectrometermeasurements. The method, moreover, is available for manysubstances which will not form crystals sufficiently large for use onthe ionisation spectrometer.Conditions necessary for makingaccurate intensity measurements on powder photographs have beendiscussed by G. W. Brindley and F. W. Spiers,6 by J. C. M. Brentano,'and by B. W. Robinson.'" Precise measurements of lattice constantsand the geometrical and other errors which arise in such measure-ments are reviewed by several authors.8 Various methods have beensuggested 9 for reducing the exposure times required for powderphotographs.New forms of camera suitable for use a t low temper-atures or where the crystal must be kept in a vacuum have beendescribed by E. Pohland lo and by B. Ruhemann.113 A. H. Compton and S. K. Allison (Macmillan, London, 1935).4 M. J, Buerger, 2. Krist., 1934,8S, 356; (Miss) D. M. Crowfoot, ibid., 1935,Phd. Mag., 1934,18, 729.6 Proc. Physical SOC., 1934, 46,, 841.7 0 Proc. Roy. Xoc., 1934, [ A ] , 147, 467.8 M. U. Cohen, Rev. Sci. Instr., 1935,6,68 ; J. Koppel, J. Phys.Radium, 1934,5,145 ; A., 1934, 587 ; E. R. Jette and F. Foote, J . Chem. Physics, 1935,3,605.9 W. E. Schmid, 2. physikal. Chem., 1933, [B], 23,347; A., 1934,162; J. P.Blewett, J . Sci. Imty., 1934, 11, 148; A., 1934, 624; A. Rogozinski, Compt.rend., 1934, 198, 963; A., 1934, 503.90, 215.Ibid., 1935, 47, 932; A., 1306.10 2.physikal. Chem., 1934, [B], 26, 238; A., 1934, 985.11 Physilcal. 2. Sovietunion, 1935, 7, 572EVANS : CRYSTALLOGRAPHY, 195The great power of X-ray methods, and especially of the powdermethod, in attacking many problems of a more general characterthan those involved in pure structure analysis, is a t last beingrecognised. Such varied problems as a qualitative and evenquantitative chemical analysis of material of which only minutequantities are available, the determination of grain size in metalsand other crystalline substances, and the detection of strain incastings, have all been successfully attacked by X-ray methods.An investigation l 2 into the constitution of bleaching powder waslargely carried out by these methods, while W.P. Jesse l3 hasdescribed quantitative analyses of metal systems accurate to 1 yo. Aspecial number of the KoZZoid Zeitschrift (1935,69, Heft 3) is devotedto X-ray and electron methods in colloid science, while a popularaccount of such applications of X-ray analysis, especially in theindustrial field, has been published.l4 Yet it is true to say that thereare many investigations to which these methods are particularlysuited which are still being attacked by older and less satisfactorymeans.One important contribution has appeared during the periodunder review which promises to be of considerable value in theelucidation of complex structures. The representation of theelectron density throughout a structure, as projected on anyplane in the structure, by means of a Fourier synthesis affords anelegant means of presenting the results of a structure analysis.It is not, however, of great value in determining an unknown stmc-ture, for although intensity measurements give us the magnitudesof all the terms of the Fourier synthesis, they can tell us nothing ofthe signs.These signs can only be determined when the positionsof most of the atoms in the structure have been found by otherexperiments. A. L. Pattersonl5 has shown that, if we form theFourier synthesis, using not the amplitudes but the intensities ofthe X-ray reflexions as the coefficients of the corresponding terms inthe synthesis, the resultant plot is such that the vectors joining theorigin to each of the several peaks represent in length and direction,but not, of course, in position, interatomic distances in the structure.In Fig.2a an example of such a plot is given for hexachlorobenzene.This substance is monoclinic, and the plane of the benzene ring isnearly parallel to the (010) face. Fig. 2b shows a projection of thel4 C. W. Bunn and others, Proc. Roy. SOC., 1935, [A], 151, 141 (see this vol.,p. 158).13 Rev. Sci. Instr., 1935, 6, 47; A., 1934, 446.1 4 “ Industrial Application of X-Ray Crystal Analysis,” H.M. StationeryPhysical Rev., 1934, 46, 372; A., 1934, 1160; 2. Krist., 1935, 90, 517,Office, 1934.543; A., 1193196 CRYSTALLOGRAPHY.molecule on this face, and all the prominent peaks in Fig. 2a may bereadily associated with the corresponding interatomic distancesin the molecule.The distances in Fig. 2b give rise to the peaks inFIG. 2a.Hexachlorobenxene. Contour map of the F2(h01) series.Fig. 2a bearing the same letters. I n more complex structures, thenumber of interatom distances will be so large that only the mostprominent between the heaviest atoms will be expected to stand outFIG. 2b.Interatomic distance diagram for the C,C1, molecule.of carbon atoms, the outer of chlorines.repeated six times iia approximate hexagonal symmetry.centrosymmetrical.bearing the sa.me letters.T h e inner ring consistsT h e interatomic distances indicated areT h e molecule is actuallyThe distances in this diagram give rise to the peaks in P i g . 2aain a Patterson synthesis, and to this extent the method has itslimitations and perhaps gives little more information than would bededuced from general considerations by an experienced worker iBERNAL AND WELLS : CRYSTAL CHEMISTRY.197structural analysis. At the same time, the Patterson synthesisdoes afford the only means of giving an unprejudiced presentationof all the information which may be directly derived from theexperimental material. The method has already been applied to adetermination of the structure of nickel sulphate heptahydrate 16where it threw considerable light on the position of the nickel andthe sulphur atoms.The tedious calculations involved in the formation of a Fouriersynthesis may be considerably lightened by the methods of C.A.Beevers and H. Lipson l7 and J. M. Robertson.18 R. C. E.CRYSTAL CHEMISTRY.There have been no notable advances in general crystal chemistryin the past two years. The generd picture elaborated by Bragg,Goldschmidt, and Pauling still continues to hold the field. L.Pauling and M. L. Huggins have, however, extended their workon atomic dimensions to include covalent binding. In an importantpaper they discuss the theory of the covalent link on the basis ofthe directed bond picture. This enables them to predict themagnetic moments to be associated with the four types of bondsdiscussed, viz., the tetrahedral bonds sp3, the square bonds dsp2,the octahedral bonds d2sp3, and the 8-co-ordinate bonds d4sp3. Inthis way they are able to distinguish between ionic and co-valent bonding in complexes.For instance, they show that theFeF, complex is essentially one of ionic bonds, whereas Ii’e(CN),has covalent bonds. In a semiempirical way they construct tableswhich give an effective radius for tht! tetrahedral, square, and octa-hedral and trigonal prism radii. These tables are given below.Be.1.072 0cu.1.35Age1.53Xtandard Tetrahedral Radii.B. C. N. 0. F.0.89 0.77 0.70 0-66 0.64A1 . Si. P. S. c1.1-26 1.17 1.10 1-04 0.99Zn. Ga. Ge. As. se. Br .1.31 1.26 1-22 1.18 1.14 1.11Cd. In. Sn. Sb. Te. I.1.48 1.44 1.40 1.36 1-32 1.28Au. w* T1. Pb. Bi.1.50 1.48 1.47 1.46 1-46l6 C. A. Beevers and C. M. Schwartz, 2. Krist., 1935, 91, 157.l7 Phil. Mag., 1934,17, 855. l8 Ibid., 1936, 21, 176.2.Krist., 1934, 87, 206; A., 1934, 350198 CRYSTALLOBRAFRY.8tandard Octahedral Radii (from Pyrite-type Crystals).Valency. Fe. Co. Ni. %I 7:) 53 29I1 ............ 1-23 1.32 1.39 1.33 1.43 1.50 1.84 *III ............ 1.22 1-31 1.32 1.42 1.491.31 1.41 IV ............ 1.21* Obtained by extrapolation.Square Radii.CoI. NiII. CUIII. RhI . PdK AgnI.IrI. PtII. AuIII.1.23 1.22 1.21 1-33 1-32 1.31Trigonal prism radii : Mo, 1.37 ; W, 1.44.These radii would be better called half-bond lengths, as thecovalencies are definitely directed, and the radii of the atoms,other than covalent bonds, may be as much as twice as large.H. G. Grimm 2 has made a general survey of chemical compoundsof the type A,BB,. He has discussed the conditions which determinetheir general character-metallic, adamantine, ionic, and molecular-and has produced a table showing the known type of compoundsformed between every pair of elements in the periodic table.R.C. Evans, in translating 0. Hassel’s “ Crystal Chemistry”(London, Heinemann), has made available in English a simple andattractively written account of the subject, but one which unavoid-ably does not include much recent work. R. W. G. Wyckoff hasproduced an extremely valuable supplement to the second edition of“ The Structure of Crystals,” which gives references and beautifullydrawn diagrams to all of the important crystal structures determinedin the years 1930-1934. Pending the second edition of the“ Strukturbericht,” this is a most valuable compilation for chemistsand crystallographers, particularly because every structure iscritically examined and those described may be considered to bewell established.MeiaZZic 8tructures.-Our knowledge of the electronic theory ofmetals, discussed earlier in this Report, has been of great assistancein understanding the crystal structure of metals and alloys, and has,in general, justified the empirical classification put forward inprevious reports. Three main factors are found to influence thesestructures : the sizes of the atoms, the number of electrons per atomin the phase as a whole, and the heterogeneity of the atoms composingthe alloy.Most of the alloy structures investigated earlier had atoms ofapproximately the same size, and consequently this factor did notenter into consideration.The three types of alloy distinguishedAngew. Chem., 1934, 47, 53; A., 1934, 234BERNAL AND WELLS : CRYSTAL CHEMISTRY. 199were those in which the atoms wcre of the same electronic type,which gave rise to unbroken solid solutions, such as the systemgold-silver; those in which the atoms had a different number ofelectrons, and consequently where the average number of electronsper atom varied with the concentration-these are the substanceswhose structures obey the Hume-Rothery rules now explained byJones-and finally, alloys where the difference of the number ofelectrons is very great, sometimes tending to pass over into semi-metals. The sequence, as given hy U. Dehlinger3 in a generalreview of metallic mixed crystals and compounds, is as follows:Mixed crystals, super-structures, inter-metallic compounds, corre-sponding to increasing affinity, a diminished region of homogeneityand an increasing difference in physical properties and crystalstructure compared to the component metals.No hard and fastlines can be drawn between these different types of combination,and this gives metal chemistry a particularly indefinite character.The r61e of differences in atomic size is beginning to be apparent.Two compounds have been known for some time, vix., Cu,Mg andZn,Mg, which may be described as close-packed structures of copperor zinc respectively with cubic and hexagonal close-packed latticesin which a large magnesium atom is inserted in the place of twocopper or zinc atoms.These types are now found to have a farwider significance, and to occur, in fact, in nearly all cases where theradii of the atoms concerned are in a, ratio of between 1 : 1-15 and1 : 1.3, or a volume ratio of approximately 1 : 2. Thus, F. Lavesand K. Lohberg * have pointed out that ME,, ZrW,, PbAu,, CuBe,,and MgNiZn belong to the MgCu, type, while MgNi,, MgCuAl,FeBe, belong to the MgZn, type. The occurrence in these lists ofmetals of a totally different chemical nature shows that thestructures cannot be due to any electronic factors, but are simplythe expression of the nearest approach to close-packing which canbe made by atoms of widely different atomic volume. They maybe regarded as substitution compounds or solid solutions in whichone atom of one type replaces two of another and, as Laves hasshown, such compounds are not confined to binary alloys.Thus thequaternary compound Mg,Zn2Cu2Ni, belongs to the Cu,Mg type,There are probably a limited number of other such compounds withdifferent volume and atom ratios : thus Zn,Mg and FeBe, possessmodifications of the Zn,Mg and the Cu,Mg structure respectively.The simplest cases of all are where adloys are of the form AB, thestructure of which is the well-known czesium chloride type, while3 Angew. Chem., 1934, 47, 621 ; 2. Metallk., 1934, 26, 227 ; %. Elektrochem.,1935, 41, 344; cf. W. E. Schmidt, 2. Metalllc., 1935, 27, 49.4 Nach. Ges. Wiss. Cottingen, 1934,1, 69200 ORYSTALLOGRAPHY.A1,Cu is an example of a type in which the small copper atoms arepacked in the interstices of a deformed cubical close-packing ofaluminium atoms.Further research will undoubtedly bring tolight many more such compounds. They are likely to show amuch more definite composition than those in which the atom sizesare more equal. But this is a purely geometrical fact, and does notdepend on any greater chemical affinity between the elementscomposing them.The existence of an intermetallic compound may be due to threereasons by no means inutually exclusive. In the first place, it maybe due simply to the existence in some simple ratio of atoms ofdifferent kinds. Such compounds will range from the orderedclose-packing discussed above to the definite structures due toatoms of unequal sizes.Secondly, it may be due simply to theaverage number of free electrons available per atom, but this islikely to have a determining effect on the structure only when theatomic sizes are approximately equal. Thirdly, it may depend onthe existence of loosely held electrons in one atom and electronaffinity in the other. This will lead to further definite compoundswhich are strictly not all of a metallic character, such as Mg,Pb.Modern methods of the exact measurement of lattice dimensionshave made it possible to get a closer view of the nature of inter-metallic solid solution. E. R. Jette,5 in a study of available inform-ation, shows that solid solutions can be divided into three types, inall of which the lattice constants are less than, equal to, or greaterthan that expected from Vegard's law : a = aAFA + a,$',, whereP denotes atomic fractions.A smaller lattice constant indicatesthe special attraction between unlike atoms, a larger one a specialattraction between like atoms. The former is shown by thesystems Ag-Pb, Ag-Pd, Cu-Ni, and Cr-Fe, the latter by Cu-Au,Cu-Pd, Cu-Ag., . .Ag-Cu, Fe-Cr, and with Au-Pt, Au-Pd, Mo-W,Pt-Ir, Pt-Rh, Sb-Bi, there is no sensible deviation from Vegard'srule. The negative and positive variations can be correlatedvery roughly with the slope of the liquidus curve tending to beconvex for negative, and concave for positive deviations, as mightbe expected.The use of high-precision determination of lattice constants willsoon become the most reliable gauge of purity of a metallic element.E.R. Jette and F. Foote have determined the lattice constants ofspecially Pure M , Ni, Ag, Au, si, Be, Mo, W, Mg, Zn, Cd, Sb, Bi, andSn, with a general accuracy of 1-2 parts in 40,000. Similar, butless accurate, determinations of other elements have been carriedti Arner. I n s t . Min. Met. Eng., 560 E.J. Chern. Physics, 1935, 3, 605201 BERNAL AND WELLS : CRYSTAL CHEMISTRY.out by E. Owen, L. Pickup, and I. 0. Rioberts 7 and M. C.Neuburger .8New super-structures Au,Mn and AuMn, face-centred and body-centred tetragonal respectively, have been found to be precipitatedat low temperatures from the extended solid solution of manganese-g0ld.9 The only compounds of the transition metals which showdefinitely novel structures are the related substances Fe,W andPe,W6, and the corresponding molybdenum compounds determinedby H.Arnfelt and A. Westgren.lo In these structures there seemsa definite tendency for tungsten or molybdenum atoms to associatein groups of two or four.The interstitial compounds have been further investigatedwithout, however, any startling discovery. Further work has beendone on the solubility of hydrogen in the transition metals,ll andthe essentially protonic nature of the solution confirmed. Thestructure of steel is now, thanks to X-ray work, fairly firmlyestablished. G. H&gg l 2 has finally shown, by careful measure-ment of lattice parameters, that the only martensite formed byquenching of austenite (face-centred y-iron containing carbon) hasa tetragonal structure which gradually approximates to cubica-iron with decrease of carbon content.The rate of decompositionof the martensite is shown to depend primarily on the temperature,but it is appreciable even at 100". An excellent popular accountof our present knowledge of the structure of steels is given byI(. van Horn.13 A higher carbide of iron, Fe,C, has been described.14The highest carbide of nickel so far found is Ni3C,15 which consistsof a hexagonal close-packed nickel structure with statisticallydistributed carbon atoms.A study of the system Fe-Cr-N 1s shows only, besides the knowniron nitrides, two chromium nitrides, Cr,N, hexagonal, and CrN,cubic face-centred; but in the Fe-Al-C system l 7 a new phaseFe,AlC, is found, face-centred cubic, in contrast with the body-centred Fe,Al.A certain solubility of carbon in platinum has heen7 2. Krist., 1935, 91, 70.9 H. Bumm and U. Dehlinger, Metallwirt., 1934, 13, 23.10 Jernk. Ann., 1935, 185.11 H. Mundt, Ann. Physik, 1934, [v], 19, 721 ; A., 1934, 590; D. P. Smithand G. J. Derge, Trans. Electrochem. SOC., 1934,66, 25 ; A.9 1934, 1168 ; M. H.Hey, J., 1935, 1254; A., 1322; J. Franclr, Nach. Ges. Wiss. GGttingen, Math.-phys. KI., 1933, 293; A., 1934, 1168.12 J . Iron Steel Inst., 1934, 11, 439; cf. J. Bpkhal and F. Cabicar, GoZZ.Czech. Chem. Comm., 1934, 6, 251; A., 1!334, 953.13 Metal Progress, Aug. 1035.16 J. Schmidt, 2. anorg. Chem., 1933-34, 216, 85.16 S.Eriksson, Jernk. Ann., 1934, 630.17 F. R. Morral, J . Iron Steel Inst., Sept. 1934; A., 1934, 1166.* Ibid., 92, 313; 1936, 93, 1.1 4 G. Hiigg, 2. Krist., 1934, 89, 92.6 202 CRYSTALLOGRAPHY.reported.18 The complex structures of the carbides of chromiumCr,C, and manganese Mn7C, with 80 atoms in the cell have beenworked out by A. Westgren.lg They consist of carbon placedinterstitially into a distorted metal framework. The silicidesof the transition metals have also been studied, particularly byB. Bor6n.20 Cr, Mn, Co, and Ni all form compounds of the typeMSi, showing the FeSi structure. The isotropic Mn,Si, alsostudied by F. Laves,21 is interesting as a simple body-centredstructure in which manganese and silicon atoms occupy all positionsindiscriminately. In Co2Si there is an arrangement of siliconchains similar to those existing in Cr,C,,22 the Si-Si distance in thechains being 2.15 A.23Electron Compounds.-No full account of X-ray studies of thisfield is given, as it is covered by the Report on non-ferrous alloys(p.165). Only references will be made to newly established crystalstructures.Now that the theoretical basis for Hume-Rothery’s rules hasbeen established (see above), special interest attaches to the studyof solubility limits of the system copper-silver, and the B-groupelements including gallium, germanium, and indium. 24 In all caseswhere large differences of atomic size do not occur, the equilibriumdiagrams depend on electronic and not on atomic proportions asthe theory demands. I n the nickel-zinc system 25 the tetragonalphases p and y correspond approximately to the fi-brass and E tothe y-brass type.Ferromagnetic Heusler alloys, Mn-Al-Cu, arefound to belong essentially to the P-type, with a regular super-structure.26 A. J. Bradley and J. W. Rodgers 27 bave used anextremely ingenious method to differentiate the positions of thecopper and manganese atoms. These are normally indistinguishableby X-rays, but by using iron, copper, and zinc K radiation, anomaliesin the scattering power of the elements in relation to the positionof their absorption edges enable the distinction to be made.18 L. J. Collier, T. H. Harrison, and W. G. A. Taylor, T r a n s . Faraday SOC.,1934, 30, 581 ; A., 1934, 987.Jernk.Ann., 1935, 231.2o ArEiv Kemi, Min. Geol., 1934, 11, A , No. 10; A., 482.21 2. Krist., 1935, 89, 189.23 B. Boren, S. StAhl, and A. Westgren, 2. physikal. Chem., 1935, [B], 29,231; A., 1194.24 W. Hume-Rothery, G. W. Mabbott, and K. M. C. Evans, Phil. Trans.,1934, [ A ] , 233, 1 ; A., 1934, 725.25 K. Tamaru and A. Osawa, Bull. I n s t . Phys. Chem. Res. Japan, 1934, 13,13; A., 1934, 482; Sci. Rep- T&oku Imp. Umiu., 1934, 23,794; V. Caglioti,Atti Congr. naz. Chim., 1933, 4, 431; A., 1934, 1166.22 See Ann. Reports, 1933, 30, 390.2 6 0. Heusler, 2. Metallk., 1933, 25, 274; A., 1934, 357.2 7 Proc. Roy. Soc., 1934, [ A ] , 144, 340; A . , 1934, 590BERN& AND WELLS : CRYSTAL CHEMISTRY. 203New p- and 7-phases have been found in the copper-gallium 28 andcopper-indium 29 systems, but anadogous compounds do not occurin the silver-indium system.30 The y-structure which occursanomalously for CuHg has been confirmed.31New compounds and new structures have been found in theFe-A1 system.32 The compounds FeAI,, Fe2A15, and FeA1, are allhighly complex; FeM3 has a moiioclinic cell of dimensions 47.4,15.4, 8.1 ,&., containing 400 atoms.33 The platinum-thalliumsystem contains one compound PtTl with a new and unusual struc-ture.34 The purple compound AuAl, proved t o have a simplefluorite type of structure,35 which may have some relation to itsunusual physical properties.The silicides of the B-group metalshave been much studied ;36 one, C U ~ ~ S ~ ~ , has a cubic cell containing76 atoms.Compounds where large differences of atomic size occurhave also been studied;37 in particular, L. Misch has studied thecompounds of beryllium with copper, nickel, and iron :38 CuBe andNiBe have the czsium chloride structures, CuBe, and NiBe, are ofthe MgCu, type, and FeBe, is of the MgZn, type ; while Ni,Be2, andPt5Be2, have a deformed y-brass structure.Our knowledge of the alloys ofthese metals has been considerably extended. U. Dehlinger 39has made a useful survey of the known alloy structures and solidsolutions of the elements Be, Mg, Zn, Cd, Hg, Al, and Sn. Itappears quite definitely that the factors conducing to extendedsolid solution are similarities in electronic constitution rather thanmere equivalence of atomic size.F. M. Jaeger and J. E. Zanstra 40Alloys of A- and B-group metak.2 8 F. Weibke, 2. anorg. Chem., 1934, 220, 293.29 F. Weibke and H. Eggers, ibid., p. 273.30 Idem, ibid., 1935, 222, 145; L. K. Prove1 and E. Ott, J . Amer. Chem. SOC.,31 F. Schoszberger, 2. physikal. Chem., 1935, [B], 29, 65.32 A. Osawa, Sci. Rep. Tbhoku Imp. Univ., 1933, 22, 803; A., 1934, 137;Kinz. no Kenk., 1933,10,432; A., 1935, 158.33 E. Bachmetew, 2. Krist., 1934, 89, 575.34 E. Zintl and A. Harder, 2. Elektrochem., 1935, 41, 767.36 C. D. West and A. W. Petersen, 2. Krist., 1935,88, 93.36 E. R. Jette and E. B. Gebert, J . Chem. Physics, 1933, 1, 753 ; A., 1934,137; F. R. Morral and A. Westgren, Arkiv Kemi, Min. Oeol., 1934, 11, [B],No. 37 ; A , , 1934, 1165; K.Sautner, Porschungsarb. Metallk. Riintgenmet.,No. 9 ; A., 1934,482 ; S. Fagerberg and A. Westgren, Metallwirt., 1935,14,265.37 V. G. Sederman, Phil. Mug., 1934, [vii], 18, 343; A., 1934, 953; H.Perlite, Keemia Teated, 1934, 2, 11; A.., 1934, 1064; C. Dbgard, 2. Krist.,1935, 90, 399 ; A., 1198 ; T. Jurriaanse, ibid., p. 323.1935, 57, 228.38 2. physikal. Chem., 1935, [B], 29, 42.39 2. Elektrochem., 1935, 41, 20.PTOC. K. Akad. Wetensch. Ameterda,m, 1933, 36, 636 ; F. M. Jaeger and E.Rosenbohm, ibid., 1934, 37, 67 ; Rec. trav. chirn., 1934, 53, 451 ; A., 1934,589204 CRYST~OGRAPBY.have made a, detailed study of the allotropy of beryllium; themetastable form at 600" is orientated parallel to the original beryl-lium crystals and must be in some sense a super-lattice of dimensionsa = 7-1, c = 10.8 A.Such a lattice would contain about 60 atoms,and the exact determination of this structure would have greattheoretical interest.The alloys of lithium have been extensively studied, chiefly byG. Grube, E. Zintl, and their collaborators.there is no true compound formation, but the solid solution ofcomposition LiMg, cannot take up any more magnesium, andfunctions towards it as a true compound. Apart from the com-pound LiZn,42 with the NaTl structure, another compound Li,Zn,is formed of a pseudo-hexagonal close-packed structure. Thelithium-cadmium alloys have given rise to considerable controversy.It appears, however, that both sides may be right : that the quenchedLiCd has a true cEsium chloride structure, as A.Baroni 43 maintains,and that the tempered alloy has the more ordered NaTI structure.44Two more compounds, LiHg, and Li,Hg, have been established,and hexagonal and cubic structures have been determined.45LiAl 46 has an NaTl structure. The structure Mg3Al, is of excep-tional interest, for here among the A-group metals we have the samecomplicated structure with 58 atoms as is found in a-manganeseand p-chromium. F. Laves, K. Lohberg, and P. Bahlfs47 havemade a complete determination of the structure; each magnesiumatom is surrounded by 4-7 other magnesium atoms at a distance of2-95-335 d., and by 6-12 aluminium atoms at a distance of2.9-3.2 A. The aluminium atom, on the other hand, besides its8 magnesium neighbours, has 2 aluminium neighbours, one at2-82 and one a t 2.65 A.This distance is very much shorter than theA1-A1 distance of 2.86 in the metal, and indicates the extent of aspecial binding force of the aluminium, such as occurs in metallicgallium. I n the system aluminium-zinc, it appears that at hightemperatures zinc may dissolve in aluminium t o the extent of48% at 350°, but at lower temperatures this solid solution splitsup into a p, aluminium-rich, and a y, zinc-rich, portion.48 Tho41 G . Grube, H. V. Zeppelin, and H. B u m , 2. Elektrochem., 1934, 40, 143,4 2 E. Zintl and A. Schneider, ibid., 1935, 41, 764.43 Ibid., 1934,40,565; AttiR. Accad. Lincei, 1934, [vi], 19,607; A., 1934, 954.44 E. Zintl and A. Schneider, 2. Elektrochem., 1934, 40, 107.4 5 Idem, ibid., 1935, 41, 771.46 G.Koinovsky and A. Maximov, 2. Krist., 1936,92,275.4 7 Nach. Ges. Wiss. CBttingelz, 1934, 1, 67.4 8 E. Schmid and G. Wassermann, 2. Metallk., 1934, 26, 145; A., 1934,1064; E. A. Owen and J. Iba11, Phil. Nag., 1934, [vii], 17,433; A., 1934, 356.I n the Li-Mg system160; A., 1934, 591BERNAL AND WELLS : CRYSTAL CITEMISTRY. 205structure of Al,Ba 49 is of some interest. It appears to be a tetra-gonal layer lattice in which each barium atom is surrounded by16 aluminium atoms, and each of the latter is surrounded by 4 bariumand 4 or 5 aluminium atoms.The structure of gallium proposed by Laves 5O has been confirmedby Bradley.5I He finds the cell dimensions to be 4.5167, 4.5107,and 7.6448 A., the smallest known departure from tetragonalsymmetry.A.tilander 52 has studied thallium compounds extensively byelectrochemical and X-ray methods. The T1-Hg system containstwo compounds of the approximate composition Hg,Tl and HgTlswith face-centred and body-centred cubic lattices respectively.The Pb-T1 system shows an extended solid solution from lead upto 92% of thallium, with some evidence for ordered structure ofT1,Pb. The compound Bi,T1 has a very interesting structure.The cell is hexagonal, a = 5-67, c = 3.37 ,&., and contains a graphite-like arrangement of bismuth-hexagons in the holes of which, aboveand below, fit the thallium atoms. The structure of TlSb,, deter-mined by F. R. Morral and A. Westrgren,53 has a somewhat deformedcssium chloride super-lattice ; each antimony atom has four thalliumneighburs at 3.1 A., one at 3.38, and four more at 3.48 A.TheSn-As system 54 has been shown to have only one compound, SnAs,with the sodium chloride structure as with SnSb. This compoundhas, however, a range of solid solubility from 34 t o 48% (by wt.) ofarsenic. It is interesting t o note that the lattice dimensionsincrease in both directions on departing from the idea1 configuration,The structure of the alloys of the rare-earth metals has beenextended chiefly by the work of A. Rossi and his collaborators.55Two types only are found, the cubic face-centred type AB,, whereA = Pr, La, or Ce, and B = Mg, Sn, T1, or Pb, and the czesiumchloride type found €or NdAl and LaMg. Praseodymium is foundto have two structures : a-Pr, fmce-centred cubic, a = 5-10, andPPr, hexagonal elose-packed, a = 5-17, c/a = 1-633.Adamantine Compounds .-Carbides, nitrides, etc.Our knowledge of4D K. R. AndressandE. Alberti, Z.1MetallL., 1935, 27, 126.51 2. Krist., 1935, 91, 303.52 2. physikal. Chem., 1935, [A], 171, 425; 1934,168, 274; A., 1934, 724;=3 8vensk Kern. Tidskr., 1934, 46, 153; A., 1934, 1296.54 W. H. Willott and E. J. Evans, Phil. Mag., 1934, [vii], 18,114; A., 1934,953.6 5 GTazzetta, 1934, 64, 748, 774, 832, 855; A., 1935, 151, 152 ; A. RosrJi andA. Iandelli, Atti R. Accad. Lincei, 1934, [vi], 19, 415; A., 1934, 720; C. W.Stillwell and E. E. Jukkola, J . Amer. Chem. Soc., 1934, 56, 56; A . , 1934, 243.See Ann. Reports, 1933, 30, 293.2.Krist., 1934, 89, 89; A., 1934, 1301206 CRYSTALLOGRAPHY.the structure of the non-metallic carbides and nitrides has been muchadvanced by the work of M. von Stackelberg. According to him,56these structures can be most readily understood by considering themas ionic, carbon, nitrogen, etc., functioning as large anions C4-, N3-,or in higher carbides as the C> or Ck ions. These ions are in generalclose-packed, the metal ions occupying octahedral or tetrahedralholes. Thus, Be,C 57 has an antifluorite structure, each berylliumhaving four carbon neighbours, and each carbon eight berylliumneighbours.carbides with separated atoms yielding methane, those with carbonpairs, acetylene, and Mg,C,, allylene, possibly owing to C, groupsin the crystal.The structure of Li3N 59 is not, as previously supposed,6O similar tothat of ammonia; it consists of a simple hexagonal arrangement ofnitrogen atoms with lithium atoms lying, some between two and somebetween three nitrogen atoms.61 Ca3N, may have a similar struc-ture. The structure of A14@, 62 has been most fully worked out :it has a rhombohedra1 cell, a = 3-325, c = 24-94 A.; the structureis a layer one, three layers of carbon atoms being interleaved withfour of aluminium. Each of the latter is surrounded by fourcarbon atoms at a distance of 1.9-2.0 A. (sum of atomic radii,2.03 8.), while the carbon atoms have either five or six aluminiumneighbours. The closely related AI,C3N63 has a very similarhexagonal structure, a layer of A N being sandwiched between theA14C3 layers.More definitely adamantine is boron carbide, B,C,examined by F. Laves.64 L. Pauling and S. Weinbaum65 havedetermined the parameters of the framework structure B6Ca 66 andfind that each boron atom is exactly 1.716 L f . from five others.It is thebest layer lattice that we know, and the two-dimensional macro-molecules of which it is made can enter into many combinationswithout affecting its structure. That all forms of carbon exceptdiamond contain such molecules has been conclusively shown byThis classification is borne out by the action ofGraphite and its compounds have been much studied.5 6 8. physilcal. Chem., 1934, [B], 27, 53.6 7 M. von Stackelberg and F. Quatram, ibid., p. 50.68 J.Schmidt, 8. Elektrochem., 1934,40,170; A., 1934,614.59 E. Zintl and G. Brauer, ibid., 1935, 41, 102.6o R. Brill, 2. Krist., 1927, 65, 94.61 H. Hartmann and H. J. Frohlich, 8. anorg. Chem., 1934, 218, 190; A,,62 M. von Stackelberg and E. Schnorrenberg, 2. phy8ikaZ. Chem., 1934, [B],63 M. von Stackelberg and I(. F. Speiss, ibid., 1936, [A], 176,140.64 Nach. Ges. Wiss. Cfcittingen, 1934,1,67.6 5 Z. Krist., 1934, 87, 181; A., 1934, 243.6 6 See Ann. Reports, 1933, 30, 394.1934, 741.7, 37207 BERNAL AND WELLS : CRYSTAL CHEMISTRY.B. E. Warren6' by Patterson-Pourier methods (see p. 195).The finest and most amorphous carbon black is found to consist ofcrystallites about 60 8. wide by 10 A. thick, containing only twoor three layers of 400 rings each.Other work on different types ofgraphite68 confirms this, and also shows that as the particle sizediminishes, the inter-layer distance increases from 3.4 to 3.6 A.The magnetic anisotropy of graphite is even greater than has beensupposed. Indian workers 69 have shown that the principalsusceptibilities are - 22.8 and - 0.4 parallel to and perpendicularto the hexagonal axes. U. Hofmann 70 has given a general surveyof the reactions of graphite; in particular, of the formation ofgraphite oxide by the addition of oxygen atoms (probably hydroxy-groups) on each side of the molecule. A series of graphite sulphateshas also been prepared 71 with sulphate groups between every two,four, six, etc., graphite planes. Carbon subfluoride, CF, is also agraphite compound which has largely lost its metallic character.72Iodides, phosphides, etc.The iodides and mercuri-iodides ofsilver and copper have proved to be of great theoretical interest(see p. 188). The p- and the y-form of silver iodide, stablebetween 146-136" and below 135", have zinc blende and wurtzitestructures respectively, with densities 5.71, and 5.69,.73 They maybe considered as close-packed iodine lattices with metal atoms intetrahedral interstices. The a-form, investigated by L. W. Strock,74has a body-centred cell, a = 5.034 A., with a density of 6.00 andtwo molecules per cell. The silver atoms cannot be placed; theyare, so to speak, in a gaseous state between the iodine atoms. Thisstructure goes far t o explain the large self-diffusion, electric con-ductivity, and plasticity of the crystals, but the structure is soanomalous that it calls for further physical and crystallographicinvestigation. A similar but less marked indeterminacy has beenfound in the cubic (> 90") modification of silver and cuprous mercuri-6 7 J .Chem. Physics, 1934, 2, 551 ; A., 1934, 1160.6 8 P. C. Mukherjee, 2. Physik, 1934,88, 247; A., 1934, 577; M. Miwa, Sci.Rep. Tdhoku Imp. Univ., 1934,23,242 ; A., 1934, 835 ; W. S. Wesselowski andK. W. Wassiliew, 2. Krist., 1934, 89, 156.69 K. S . Krishnan, Nature, 1934, 133, 174; B. C. Guha and B. P. Ray,Indian J. Physics, 1934,8,345.70 Kolloid-Z., 1934, 69, 351 ; A., 1935, 163 ; U. Hofmann, A. Frenzel, andE. Csal&n, Annalen, 1934,510,l; A., 1934, 614; cf.H. Thiele, 2. Elektrochem..1934, 40,26; A., 1934, 262.7 1 A. Frenzel and U. Hofmann, ibid., p. 511 ; A., 1934, 978.72 0. Ruff and 0. Bretschneider (with F. Ebert), 2. anorg. Chem., 1934,217,73 N. H. Kolkmeijer and J. W. A. van Hengel, 2. Krist., 1934, 88, 317; A.,74 2. physikal. Chem., 1934, [B], 25, 441 ; A., 1934, 834.1 ; A., 1934, 378.1934, 1161 ; L. Helmholz, J . Chem. Physics, 1935, 3, 740208 CBYSTALLOGIRAPHY.iodides studied by J. A. A. Ketelaar : 7 5 s 76 neither mercury nor silveratoms are in fixed positions in the cubic close-packed iodine lattice.The structures of a number of phosphides and arsenides havebeen determined by M. von Stackelberg and R. Paulus.77 Zn3P,,Zn3As,, Cd3P,, and Cd,As, have not, as was previously supposed, acubic, but a tetragonal pseudo-cubic, structure in which the metalatoms fit in the tetrahedral holes of a slightly deformed cubic closepacking.ZnP,, CdP,, and ZnAs, have more complicated tetragonalstructures. The structures of Cu,Sb and Fe,As are identical ; theymay be considered as layers of cubic close-packed CuSb, Cu2, CuSbheld together by attractions between the copper in one layer and theantimony in the next.78 The monophosphides and arsenides of Mn,Fe, Co '9 are shown to have a modified NiAs structure, while FeP,has a marcasite structure.*0The work of the past two years hashelped to confirm and extend the general classification put forwardin the Report for 1933 (p. 398). W. Hofmanngl has studied, inparticular, the sulphaiitimonatcs, and shown that where the ratioSb : S < 1 : 3, there is a tendency t o form fibrous crystals with achain period 3 0 8 4 .3 A. corresponding to the chain molecules s s sSulphides and sulpho-salts.s s sThere is a general tendency for antimony to have three close sulphurneighbours, copper four, and lead six.A. Ferrari has shown that the series, sclericlase PbAs,S, to dufres-noyite Pb&ssS5, is isomorphous and shows a strong resemblance toorpiment As,S, and to wolfsbergite CuSbS,.fj2 Many more sulphidesare found t o be related to the zinc blende 4-co-ordination type.Binnite (Cu ,Fe)12As4S13, analysed by L. Pauling and E . W. Neuman,83may be taken as the type of the tetrahedrite minerals; here again,the arsenic atoms are attached to 3 sulphur atoms only.Colusite(Cu, Fe, Mo, Sn),(S, As, Te),-484 has a statistical zinc blende76 2. Krist., 1934, 87, 436; A., 1934, 947.76 2. physikal. Chem., 1934, [B], 26,327 ; 1935,30,53.7 7 Ibid., 28, 427.78 E. Elander, G. HLigg, and A. Westgren, Arkiv Kemi, Min. Geol., 1935,79 K. E. Fylking, ibid., 1934,11, [B], 48.80 K. Meisel, 2. anorg. Chem., 1934,218, 360; A., 1934, 947.81 2. Krist., 1935, 92, 161.82 A. Ferrari and R. Curti, Per. Min., 1934, 5, 3.O3 2. Krist., 1934, 88, 54; A., 1934, 1060.84 W. H. Zachariasen, Amer. Min., 1933, 18, 534; A., 1934, 720.12, [B], 1BERNAL AND WELLS : CRYSTAL CHEMISTRY. 209structure. Stannite, Cu,FeSnS4,85 belongs to the chalcopyritetype, while enargite, Cu,AsS4,*6 is more closely related to wurtzitebut contains separate ASS, groups.Tetradymite, Bi,Te,S,87 has avery interesting structure with successive layers of S-Bi-Te-Te-Bi-Sall in 6-co-ordination, For other sulphides examined, only refer-ences can be given.** Silicon disulphide has a structure of a newtype. W. Bussem, €3. Fischer, and E. Gruner 89 have found that > Si/'\si \s/ <:x:>i<it contains chains of tetrahedra sharing pairs of sulphur atomsand not a three-dimensional network as in SiO,.Ionic Compounds.-Halides. E. Zintl and A. Harder Q0 have com-pared the structures of LiHl and LiH2, the respective latticedimensions being 4.085 and 4-065 & 0.001 8. This means thatthe radius of the hydrogen ion is changed from 1.27 to 1-26, or0.8% effectively, by the lower zero-point energy of deuterium.They 9 l have further examined tho hydrides of calcium, strontiumand barium, and shown that these possess a pseudohexagonalstructure intermediate between a CaF, and a layer lattice.Eachstrontium ion has three hydrogen neighbours at 2.35 and four at2.71 A. (sum of ionic radii, 2.52 A.).E. B. Thomas and L. 5. Wood 92 have examined the reactionsbetween alkali halide pairs. In every case but two, the final productcontains the pair with the smallest radius sum and therefore withthe largest lattice energy, e.g., NaBr + KC1 --+ NaCl + KBr.In the two cases indeterminate, ICBr + RbI and RbCl + CsBr,homogeneous solid solutions are formed.Although calcium chloride has a slightly deformed rutile struc-ture,gs the halides of the other bivalent elements cadmium, cobalt,and nickel have been shown 94 to have either the cadmium chloride85 L.0. Brockway, Z. Krist., 1934, 89, 434; A., 1935, 152.86 L. Pauling and S . Weinbaum, ibid., 88,48; A., 1934, 1060.D. Harker, ibid., 89, 175.M. J. Buerger, Amer. Min., 1935, 20, 36; A., 323; F. Weibke and J.Laar (with K. Meisel), 2. anorg. Chem., 1935, 224, 49; A., 1322; G. R. Leviand A. Baroni, 2. Krist., 1935,92,210 ; B. Gossner and 0. Kraus, Centr. Min.,1934, [A], 1, 1 ; B. Gossner, ibid., 1935, [A], 11, 321.Naturwiss., 1935, 23, 740.90 2. physikal. Chem., 1936, [B], 28, 478.91 Z. Elektrochem., 1935,41, 33.92 J . Amer. Chem. SOC., 1935,57,582; A., 832; 1934,56,92; A., 1935, 265.93 A. K. Van Bever and W.Nieuwenkamp, 2. Krist., 1936, 90, 374.94 J. M. Bijvoet and W. Nieuwenkamp, ibid., 1933, 86, 466; A., 1934, 16;J. A. A. Ketelsar, ibid., 1934, 88, 26; A., 1934, 1060; H. Grime and J. A.Santos, ibid., p. 136; A., 1934, 1161210 CRYSTALLOGRAPHY.or the cadmium iodide structure or to alternate between them (seep. 188). G. Bruni and A. Ferrari95 have discussed the extendedisomorphism of halide crystals based on close packed halogenions.96 Parallel intergrowths have been found between potassiumand lead chlorides.97H. Braekken and W. Scholten 98 have determined the structureof mercuric chloride. It is a fairly definite molecular lattice witha trace of ldyer formation, but along (120) and not along (OOl), asin mercuric bromide. The mercury halides are a good example ofthe transition from a purely ionic type, HgF,, to a molecular typeHgCl,, and through a molecular layer lattice, HgBr,, to a true layerlattice HgI,,gQ with increasing polarisability of the anion.F.A. Bannister and M. H. Hey have shown that the structureof matlockite, PbFCl,, and of PbFBr is a type structure foroxyhalides-such as BiOCl(Br,I), and probably others such asFeOC1.E. Zintl, A. Harder, and B. Dauth 3 have exam-ined the compounds (Li,Na,K),(O,S,Se,Te). All crystallise withthe fluorite structure, but there are considerable variations fromaccepted ionic radii. (Mlle.) B. Riihemann 4 has shown that thethermal anomaly of manganese oxide a t - 115" to - 119" isaccompanied by a change of lattice constant from 4.426 to 4.416.Similar anomalies have been reported for FeO and Fe,04, wherethey are accompanied by magnetic changes.These changes,though similar to those produced by rotation of molecules, are hereprobably due to electronic changes in the unfilled electron levels ofiron and manganese. Palladous oxide has been shown to have4-square co-ordination like its sulphide.5 The structure of cupricoxide, tenorite,6 is a distorted monoclinic variety of the samestructure : each copper atom is surrounded by 4 oxygen atoms in arectangle, Cu-0 = 1-95. Another form is reported.'Considerable dispute between electron and X-ray methodshas arisen over the lattice dimension of zinc oxide. G. I. FinchSimple oxides.95 2. Krist., 1934, 89, 499.g6 See Ann. Reports, 1931, 28, 285.9 7 M.Mehmel and W. Nespital, Z. Krist., 1934, 88, 345; A., 1934, 1161.g8 Ibid., 89, 448.D9 W. S. Gorski, Physikal. 2. Sovietunion, 1934, 5, 367 ; P. Joliboia and G.Fouretier, Compt. rend., 1933, 191, 1322 ; A., 1934, 41.Min. Mag., 1934,23,587 ; 1935,24,49 ; A., 1934, 1197.See Ann. Reports, 1933, 30,, 399.2. Elektrochem., 1934, 40, 588.Physikal. 2. Sovietunion, 1935, 7, 590; A., 1307.See Ann. Reports, 1933, 30, 396.G. Tunell, E. Posnjak, and C. J. Ksands, 2. Krist., 1935, 90, 120.C. A. Murison, PhiE. Mag., 1934, [vii], 17, 96; A., 1934, 134RERNAL AND WELLS : CRYSTAL CHEMISTRY. 21 1and H. Wilman 8 find by electrons, a = 3.258, c = 5.239, & 0.005 A.,whereas C. W. Bunn finds by X-rays a = 3.2426 &- 0.0001,c = 5.1948 & 0*0003 A.9 This apparent discrepancy may be dueto the dispersion of the electron waves, but another cause hasrecently been shown by V.E. Cosslett 10 to be that the dimensionsof zinc oxide prepared as smoke vary with time, a changing from3.234 to 3.279, and c from 5.221 to 5.367 in 18 months owing to slowrelief of quenching strain.G. Hagg l1 has studied the properties of thecubic tungsten bronzes Na1-o.3WO3.12 They may be consideredas interstitial solutions of Na in WO, or as solid solutions ofNa+WS+O, in WefO,. All have a sub-metallic character (surfacecolour, conductivity decreasing with temperature) which becomesmore marked as the percentage of sodium falls; when Na : W <0.3 : I, the amount of Na is not sufficient to stabilise the open cubicstructure and it becomes tetragonal, exactly as in the correspondingcase of the silicates ultramarine 13 and sodalite.l4 Correspondingsuboxides of tungsten, WSO,, and W4011, have been examined;15they may be, however, hydrogen bronzes H05WO3 and H025W03.The &,O, system also shows continuous variations of structureson taking up and losing oxygen.I6 Mn,03 exists in two forms,P-Mn203, bixbyite C type, and cc-Mn203, probably related toMn,O4 as y-Fe,O, is to Fe,O,.Nd,O, and La,03 l 7 have now beenprepared of the C (cubic) type.E. J. W. Verwey 18 has specially studied the y-Fe,O, and y-Al,O,structures. The relation of these to the spinels has been studiedby E. J. W. Verwey,l8 G. H&gg,lg E. Kordes,Z0 and others.2l It hasbeen shown, from considerations both of atomic dimensions and ofComplex oxides.* J., 1934, 751; A., 1934, 835.Proc.Physical SOC., 1935, 47, 835; A., 1307.lo Nature, 1935, 136, 988.l1 2. physikal. Chem., 1935, [B], 29, 192; Nature, 1935,135, 874.l2 See Ann. Reports, 1933, 30, 400.l3 F. M. Jaeger, Bull. SOC. frang. Min., 1930, 53, 183.l4 T. F. Barth, 2. Krist., 1932, 83, 606.l5 F. Ebert and H. Flasch, 2. anorg. Chem., 1934, 217, 95; A., 1934, 378.l6 P. Dubois, Compt. rend., 1934, 199, 1416; A., 1935, 181; M. Le Blancl7 K. Lohberg, ibid., 1935, [B], 28, 402.18 J . Uhem. Physics, 1935, 3, 592; A., 1307; 2. Krist., 1935, 91, 65, 317;l9 2. physikal. Chem., 1935, [B], 29, 95 ; G. Hligg and G. Soderholm, ibid.,2o Ibid., 91, 193 ; 92, 139.21 G.L. Clark, E. E. Howe, and A. E. Badger, J . Amer. Cemm. SOC., 1934,and G. Wehner, 2. phyaikal. Chem., 1934, [A], 168, 59; A., 1934,378.E. J. W. Verwey and M. G. van Bruggsr, ibid., 92,136.p. 88.17,7 ; A., 1934,249212 CRYSTALLOGRAPHY.intensities, that the previously assumed oxygen addition 22 to thecell is incorrect, and that, instead, there are 21Q cations distributedstatistically over the 24 (8 tetrahedral and 16 octahedral) vacantpositions in the cell. Small quantities of lithium stabilise thisstructure as LiAl,08 20 in the limit. The y’-Al,O, formed by surfaceoxidation is an even more statistical structure with the sameoxygen arrangement ; the 213 aluminium atoms occupy 32 positions,or in the reduced cell which results, 28 atoms occupy the 4 positionsof the rock salt lattice.A similar structure, but with Li& andTi$t ions instead of Alii is that of Li,Ti0,,20 which is fully misciblewith MgO and LiFeO, (see p. 188).E. Posnjak and T. F. W. Barth23 have studied the hardly lessextended haematite(Fe,O,)-ilmenite(FeTi0,) series. These areshown to be strictly isomorphous, as are the titanates of Mg, Mn, Co,Ni, and Cd (low-temperature form). The high-temperature formof CdTiO, belongs to the perovskite type, which has also verymany members.24Hydroxides. The past two years have shown great advances inour knowledge of the hydr0xides.2~ As the numbers of structuresanalysed increased, the function of the hydrogen in binding togetherthe hydroxy-groups attached to different cations was more fullyrecognised. J.D. Bernal and (Miss) H. D. Megaw26 have sum-marised our knowledge on this point in a paper where all knownhydroxide structures are discussed. It is found that the hydroxylgroup varies in a continuous way from a quasi-isotropic group inalkali hydroxides t o a definitely tetrahedral, water-like, group inthe neutral and slightly acid hydroxides. The increasing polarisingpower of the cation drives the proton further from its own oxygennucleus, and consequently increases its attraction for the negativeregions in other hydroxyl groups. In this way, a bond, which maybe called the hydroxyl bond, is formed, only leas in strength than thehydrogen bond in acids (as shown by the 0-0 distance of 2.76instead of 2-55 8.as in acids). By the use of this conception, it hasbeen possible to locate the positions of hydrogen atoms in a numberof hydroxide structures, particularly in hydrargilltite 27 where thesix hydroxyla of different Al(OH), groups form an irregular trigonalprism, six of whose sides, of length 2-78, 2.80, 2-82, and 2.94, 2.98,3.10 B., represent hydroxyl bonds, while the remaining three, ofes See Ann. Reports, 1933,30, 403.23 2. Krist., 1934, 88,265, 271 ; A., 1934, 1162.24 A, Haffmam, 2. physiEaE. C h m . , 1935, [B], 28, 65; H. Rheinboldt, J .25 Cf. Ann. Reports, 1933, 30, 401.87 (Miss) H. D. Megaw, 2. Krist., 1934, 87, 185; A., 1934, 352.pr. Chem., 1934, [ii], 139, 318; A., 1934, 587.Prm. Rmj. Sac., 1935, [A], 151, 384; A., 1307BERNAL AND WELLS : (3RYSTAL CHEMISTRY.213length 3.32, 3.38, and 3*46A., do not. Linking up of hydroxylbonds explains the properties of the gels formed by neutral hydr-oxides, discussed from the structural point of view by R. Fricke.28The structure of boric acid has been completely determined byW. H. Zachariasen.29 It consists of flat layers of BO, groupsattached to each other by hydrogen or hydroxyl bonds, the 0-0distance, 2.71, being nearer the requirements of the latter. Thelayers adhere by residual forces at a distance of 3-18 A., agreeingwith the cleavage and softness of the crystals. The hydratedboron phosphate, B( OH),, (HO),PO may have a very similar struc-ture.30Telluric acid is also a hydroxy-acid, Te(OH),; its structure hasbeen studied by B.Gossner and 0. Kraus and by L. Pauling.32In its two cubic and monoclinic (pseudocubic) forms it representsTe(0H) octahedra bound together in different ways by hydroxylbonds of length 2.76 8. Recent work on zinc hydroxide 33 shows thatthe different reported crystalline forms have all the same structure.34The oxy-hydroxide, BO(OH), has a definite crystalline form 35but its structure has not been determined. The structures ofM- and y-Al(Fe)O(OH), diaspore (goethite) and bohmite (lepido-crocite), have been determined by S. Goldsztaub 3, md F. J.Ewing.37 Both contain hydroxyl bonds, but whereas the a-formsare fairly compact, the y-forms are true layer lattices of the typeof the oxychlorides (see p. 210). The calcium aluminates formcomplex hydrates and hydroxy-compounds.3* The structure ofone of these, hydrocalumite,39 Ca,Al( OH) ,,3H,O, has been partiallyanalysed; it consists of alternate layers of A1(OH),2H20 andCa2H20.The chief interest with silicate investig-ations in the past two years has been concerned with those silicatesBorates and silicates.28 Kolloid-Z., 1934, 69, 312; A., 1935, 162.29 2.Krist., 1934, 88, 150; A., 1934, 1161.30 E. Gruner, 2. anorg. Chem., 1934,219, 181; A., 1934, 1081.3L 2. Krist., 1934, 88, 298; A., 1934, 2161.aa Ibid., 1935, 91, 367.33 K. Petrescov, ibid., p. 505; (Miss) H. 1). Megaw, ibid., 1935, 90,34 Ses Ann. Reports, 1933, 30, 401.36 H. Menzel, H. Schulz, and H. Deckert, 2. anorg. C'hern., 1934,220,49.36 Bull. SOC. f r a v .Min., 1935, 58, 6.37 J . Chem. Physics, 1935, 3, 203; cf. M. Deflandre, Bull. Sac. fra%. Min.,1932,55,140; K. Takane, Proc. Imp. Aliad. Tokyo, 1933,9,113; F. J. Ewing,J . Chern. Physics, 1934, 3,420.283.3 8 R. Salmoni, Qazzetta, 1935, 64, 519.39 C. E. Tilley [with (Miss) H. D. Megttw and M. H. Hey], Min. Mag., 1934,23, 607; A., 1934, 1197214 CRYSTALLOURAPHY.with extended three- and two-dimensional structures, i.e., withsilica in its various forms, with zeolites, and the clay minerals. NOWthat the main outline of silicate structure is known, its utility isbeing appreciated in the technical sphere ; particularly in America,much work is being done on X-ray structures in connexion with theglass and ceramic industries, which involves not only the study ofthose silicates but of the analogous boron compounds which alsoform extended frame-work structures.N. W. Taylor and S. S.Cole 40 have succeeded in producing crystalline B,O,, hithertoknown only as a glass, by careful dehydration of H,BO,. It appearsto be cubic, a = 10.04, with 16 molecules per cell, but its exactstructure is not known. It melts at 294" &- 1" to a very viscousliquid which hardens to glass at 276". On melting, there is anincrease in density from 1.805 to 1.844, showing that, like ice, butunlike silica, the arrangement of the solid has a lower effectiveco-ordination than that of the liquid.A study of the borates 4 1 shows that, like t'he silicates, the extendednetworks and chains may be found; but no complete structureshave been worked out.M. Mehmel 42 has made an elaborate studyof boracite, Mg6C1,B,4026, which above 265" is cubic, a = 12-1 8.,and below, rhombic, pseudo-cubic; but the exact structure has notbeen determined-it is apparently also of a, framework character.The structure of jeremejewite, BA18,,43 has been studied but provesto be unexpectedly complex. The structures of the phosphates andarsenates of boron, aluminium, and iron, as Goldschmidt predicted,are similar to those of silica. BPO, and BAsO,~, have a cristo-balite structure with both atoms tetrahedrally surrounded byoxygen. M. Strada4j maintains that AlPO, and AlAsO, havethe same structure. El. F. Huttenlocher 46 and F. Machatschki 47have, however, shown that normally they are of the quartz type witha doubled c axis on account of the difference of the two atoms re-placing silicon, v.Caglioti 48 has shown that FePO, has the samestructure, but the AlBO, may be dimorphous with the high-temper-ature cristobalite type, thus reconciling all the other workers' results.T. F. W. Barth49 has gone further, and shown the aluminites and40 J . Arner. Chern. SOC., 1934,56, 1648 ; A., 1934, 947 ; J . Arner. Ceram. Soc.,4 1 S. S. Cole, N. W. Taylor, and S. R. Scholes, ibid., p. 79; S. S. Cole, S. R.42 2. Krist., 1934, 87, 239; 88, 1 ; A., 1934, 387, 1060.43 B. Gossner and 0. Kraus, Centr. Min., 1934, [A], 11, 348.41 G. E. R. Schulze, 2. physikal. Chem., 1934, [B], 24,215 ; A., 1934,352.45 Gazzetta, 1934, 64, 653; A., 1934, 1296.46 2.Krist., 1935, 90,508; A., 1194.48 Atti R. Accad. Lincei, 1935, 22, 146.1935,18,55.Scholes, and C. R. Amberg, ibid., p. 58.4 7 Ibid., p. 314; A., 1060.49 J . Chem. Physics, 1935, 3, 323BERNAL AND WELLS : CRYSTAL CHEMISTRY. 21 5ferrites, K,AI,O, and (K2, Rb,, Pb)(Fe20,), also to be of the cristo-balite type with the large atoms in the interstices as in ~ a r n e g e i t e . ~ ~M. J. Buerger has discussed the stability fields for the differentforms of SiO,.51 The three forms, quartz, tridymite, and cristo-balite, have increasingly empty spaces in the structure; con-sequently, the addition of foreign atoms with appropriate siliconsubstitutions has the effect of stabilising the higher-temperatureforms. The general formula for such silicates can be writtenWhere M represents the atom substituting the silicon, usually AP,and Q* is the interstitial atom, usually Nali or Ca2+.When n = 1,the tridymite structure, and when 12 = 2 the cristobalite structure, i8stable at room temperatures.A detailed analysis of low cristobalite structures has been made byW. Nieuwenkamp; 52 the Si-0-Si angle is found to be 150". P'ei-Hsiu Wei,54 in a redetermination of the a-quartz structure, foundit to be 144". Very interesting two-dimensional crystals of cristo-balite, consisting essentially of polysynthetic twins, have beendescribed as pseudomorphs of t r i d ~ m i t e , ~ ~ the (111) plane of thecristobalite corresponding in different positions to the (0081) planeof the latter. Further work has been done on the formation ofcristobalite and the coagulation of silica gels.55B.E. Warren has made a very thorough study of the structure ofsilica and other glasses by means of X-ray~.~G The new methodsof crystal analysis (see p. 195) make it possible to determinethe relative statistical position of the silicon, oxygen, and otheratoms. The glasses of SiO,, GeO,, BeF, give essentially the samepattern. The silicon atom has six tetrahedral oxygens at 1.60, fourmore silicon neighbours a t 3.20, and twelve more SiO, groups at5.20 d. I n the case of the soda glasses, a certain number of oxygenatoms are attached to only one silicon atom, but to several sodiumatoms, each of which has on the average two oxygen neighbours at2.35 and two silicons a t 3.45 8.50 See Ann.Reports, 1933, 30, 406.51 2. Krist., 1935, 90, 186.53 Ibid., 90, 377.5 5 F. P. Dmyer and D. P. Mellor, J . Proc. Roy. SOC. N.S. W., 1934, 68, 47;A., 1935, 324; 67, 420; A., 1934. 947; M. 0. Charmandarian and V. K.Markov, Ukrain. C'hem. J., 1933, 8, 1; A., 1244.66 Physical Rev., 1934, [ii], 45, 657 ; A., 1934, 834; B. E. Warren and C. F.Hill, 2. Kyist., 1934,89,481; B. E. Warren and A. D. Loring, J . A ~ w . Ceram.SOC., 1935, 18, 269; A., 1308; cf. H. Hollenweger and H. Rumpett, Angew.Chem., 1933, 46, 662; A., 1933, 1247.52 Ibid., 92, 82.54 Ibid., 92, 355216 CRYSTALLQQRAPHY.EIectron diffraction has also been applied to the study of glasses.57N. A. Schischakov has obtained the rather surprising result that veryfinely powdered silica, glass shows sharp lines, indicating eitherthe presence of small crystals of cristobalite in normal glass, or moreprobably, the rapid devitrification of glass when ground to a finepowder.Structural work on the felspars has been c o n t i n ~ e d .~ ~ The san-idine type 69 is found to hold for the K-Ba felspars. The albite-anorthite series (NaA1Si,08 --+ CaA1,Si,Os) show a doubling of theunit cell when the number of calcium atoms is greater than that ofsodium.The structure of the zeolites has been particularly well studiedwith special relation t o their base-exchange properties ; a generalpicture of them is given in an important paper by W. H. Taylor.60The mode of binding the unattached cations and the water mole-cules is discussed, and it is found possible to place the water mole-cules in such a way as to specify the tetrahedral positive and negativelinkings postulated by Bernal and Fowler.61 J.Wyart 62 has deter-mined the structure of cliabazite and other zeolites, and an importantseries of papers has been produced by F. A. Bannister and M. H.Hey 63 correlating the chemical and structural properties of thezeolites. The deformed Al-Si framework of the structures ofhauyn and nosean, Na[A1,Si60,,]804, has been studied byMachatschki.64Clay Ji!ineruZs.-The structure of the clay minerals has excitedmuch interest, both scientific and technical, in connexion withceramics and soils. A general account of the X-ray work is givenby U. Hofmann,64a and a more popular historical survey by C.E.Marshall. 65 Owing to the fine-grained nature of clays, the problemoffers great difficulties, but X-ray methods have succeeded a t leastin ordering an apparently bewildering mass of data.J. W. Gruner 66 R. C. Ma~Murchy,~~ M. Mehmel,6s and57 N. A. Schischakov, Nature, 1935, 136, 514; A., 1309; K. R. Dixit,58 W. H. Taylor, J. A. Darbyshire, and H. Strunz, 2. Krist., 1934, 87, 464;59 See Ann Reports, 1933, 30, 405.6o Proc. Roy. SOC., 1934, [ A ] , 145, 80; A., 1934, 947.61 See Ann. Reports, 1934, 31, 42.62 Bull. Soc. franc. Min., 1933, 56, 81; A., 1934, 1197.Physilcal. Z., 1934, 35, 141; A., 1934, 352.p., 1934, 947.Min. Mag., 1933, 23, 421; 1934, 23, 483, 556; A., 1934, 167, 508, 882;64 Centr.Min., 1934, [A], 5, 136.6 5 Science Progress, 1936, [v], 30, 422.66 2. Krist., 1934,88,412; A,, 1934, 1162; Arner. Min., 1934,19,557; A,,13? 2. Krist., 1934, 88, 420; A., 1934, 1162.1935,24,99; A., 1345.See ref. (70), p. 207.1934, 841 ; 1935,20,475; A., 1345.6 8 Ibid., 1935, 90, 53BERNAL AND WELLS : CRYSTAL CHEMISTRY. 217others 69 have made more or less complete structure analyses. Thereare roughly three series of clay minerals containing treble, double,and single (SiAl),O, and Al,Mg,(OH), hexagonal layers. They differfrom the micas in that the layers are electrically neutral and arejoined only by hydroxyl bonds. The treble series is represented bytalc and pyrophyllite, with two Si,Os layers on either side ofMg,(OH), layer (talc) or A1,(OH)6 layer (pyrophyllite).Theformula may be written (indicating layers in turn by brackets)(O,)Si( 0,OH) ($$ (O,OH)Si(O,). By intercalating an indefinite3amount of water between such layers, the bentonite-thixotropicminerals are formed, montmorillonite (Mg), beidellite (Al), andnontronite (Fe3+). The double series has a Si,06 layer on one sideonly of the Al,(OH), layer. It is represented by kaolinite,(O,)Si( 0,0H)Al,(OH)3, and also by nacrite, dickite, and meta-halloysite, which differ only in relative positions of the layers.The single-layer clays are represented by halloysite, which hasalternate silica alumina sheets joined by hydroxyl bonds,here also water can enter between the layers.Optical and chemical research is keeping pace with the X-ray~tudies.7~ The formulze of the minerals have been recalc~lated,~~and the main types, kaolinite, dickite, and montmorillonite, spthes-ised by R.H. Ewe11 and H. Insley 72 by heating co-precipitatedhydrogels under high pressure.The cyanide ion inAgCN does not rotate as it does in KCN,', but as C. D. West 74has shown, it forms a unique linear lattice Ag-CN-Ag-CN in whichthere is considerable freedom of motion along the lines. TheAg-Ag distance is only 5.26 8., so it is possible for Ag to be co-ordjnately linked to the CN group at either end. The peroxide ion,Oi', has been studied in the tetragonal SrO, and BaO,, isomorphouswith CaC2.75 The 0-0 distance is 1.31 (Psuling theoretical, 1.32;in persulphate, 1.46). The CNS group 7G is found to be bent c t t an69 B.Gossner, Celztr. Min., 1935, [A], 7, 195; G. Nagelschmidt, 2. Krist.,70 C. S . Ross and P. F. Kerr, U.S. Geol. Survey, 1934, Prof. Paper 186-G,71 J. Holzner, Chem. Erde, 1935,9,464; A., 1220; C. E. Marshall, 2. Krist.,72 J . Res. Nat. Bur. Stand., 1935,15, 173; A., 1333.73 See Ann. Reports, 1931, 28, 295.74 2. Krist., 1934, 88, 173; 1935, 90, 555; A., 1194.7 5 J. D. Bernal, E. Djatlowa, I. Razarnowsky, 8. Reichstun, and A. G.'6 W. Biiesem, P. Gunther, and R. Tubin, 2. physibal. Chsm., 1934, [B],. . . (0,)SiOH . . . (OH),AI,( OH), . . . . ;Complex Ions.-Diatomic and linear ions.1934, $7,120; A., 1934, 274.135; A., 1935, 322; C. E. Marshall, 2. Krist., 1935, 90, 8.1935, 91, 433.Ward, ibid., 1936,92,344.24,l; A., 1934,243218 CRYSTALLOGRAPHY.angle of 130°, but the results are not conclusive.The I,’ group ofNH41, has been carefully studied by R. C. L. Mooney ; 77 it is practic-ally straight but unsymmetrical, 1-1 distances being 3.10 and 2.82,a small but probably real difference. The 1-1 distance in differentmolecules is 4 - 1 4 - 2 8 and NH,-I 3-7 A. W. H. Zachariasen andMooney ‘8 have determined the structure of the hypophosphitegroup H2P0,; it is a distorted tetrahedron with oxygen a t twocorners and hydrogen at the others ; the 0-P-0 angle is 120”.The structure of sodium hydrogen carbonate has alsobeen determined by Zachariasen.79 The CO, groups are linkedin endless chains by a hydrogen bond of length 2.55 A. Czesium ni-trate 8o has a pseudo-cubic structure resembling CsIand KIO,.WhenNO,‘ ions are not parallel or are rotating, they behave as if they weresimple ions about equivalent to 1’, as also do the ClO,‘, MnO,‘ ions.and BeF,” 82 ions have been proved iso-morphous with the C10,’ and SO4” ions. Ce,(W04)3 83 has ascheelite, CaWO,, structure with cerium atoms statistically distri-buted. Na6(S0,),C1F, sulphohalite, is shown by A. Pabst 84 tohave an extremely compact cubic structure with SO, groups in thecube centre, C1 and F alternately a t the corners, and Na atomsmid-way along the edges.The structures of a large number of hexafluoro- andhexachloro-salts have been determined,85 but in every case theyconfirm the octahedral character of the group. The ions OsO2C1,” 86and QsNCl,” 87 also appear to be octahedral, the first in trans-configuration.L.Pauling, H. P. Mug, and A. N. Winchell 88 have shown thatswedenborgite, NaBe4Sb07, does not contain an SbO, group butconsists of SbO, groups and Be40 groups as in basic beryllium acet-AX, ions.AX, ions. The BF,’AX, ions.7 7 2. Krist., 1935, 90, 143.78 J . Chem. Physics, 1934, 2, 34; A., 1934, 243.79 Ibid., 1933,1,634; A., 1934, 16.81 J. L. Hoard and V. Blair, J. Amer. Chem. Soc., 1935, 57, 1985.82 P. L. Mukherjee, Current Sci., 1934,3,66; A., 1934, 1162; R. Hultgren,2. Krist., 1934, 88, 233; A., 1934, 1162; J. L. Hoard and V. Blair, J . Amer.Chem. SOC., 1935, 57, 1985.L. Waldbauer and D. C. McCann, ibid., 1934, 2, 615; A., 1934, 1161.83 J. Beintema, Proc.K. Alcad. Wetensch. Amsterdam, 1935, 38, 1011.8 6 B. Gossner and 0. Kraus, ibid., 88, 223 ; A., 1934, 1161 ; J. A. A. Kete-laar, ibid., 1935, 92, 155; R. B. Corey, ibid., 1934, 89, 10; R. B. Corey andIt. W. G. Wyckoff, ibid., p. 469; G. Engel, ibid., 1935,90,341; J. L. Hoard andL. Goldstein, J . Chem. Physics, 1935, 3, 645.8 6 J. L. Hoard and J. D. Grenko, 2. Krist., 1934, 87, 100; A., 1934, 2.43.8 8 Amer. Min., 1935, 20, 492; A., 1308.2. Krist., 1934, 89, 514.J. Verhulst, Bull. SOC. chim. Belg., 1933, 42, 359; A., 1933, 1235BERNAL AND WELLS : CRYSTAL CIIEMISTEY. 210ate.89 NaSb(OH),,W though tetragonal, a = 8.00, c 5 7.86, hasessentially a sodium chloride structure of Na’ and Sb(OH),’ ionsbound together in a face-centred ciibic array by hydroxyl bonds asin Te(OK),, a = 7.83 (see p.213).G. R. Levi and G. Peyronel 91 havestudied the cubic salts (Si, Ti, Zr, Sn, Hf)P,07 and have establishedthe fact that the P&- ion consists of two tetrahedra with a commoncorner and possessing the symmetry 3, trigonal axis. The strongeffects of the quadrivalent ions ma,y be in part responsible for thisregularity. It would be interesting to see what the structure of theP,07 ion would be in an alkali pyrophosphate. The trithionate ion(S,O,)2- is essentially, according to W. H. Zachariasen,92 a pyro-ionin which the linking is done through a sulphur atom (see Fig. 3).The ion has one plane of symmetry through the three sulphur atoms,FIG. 3. FIU. 4.Pyro-, per-, and poly-ions.‘ \esulphuP.0 oxyg&n.Structure of trithionate radical. Structure of persulphate group.and a pseudo-plane perpendicular t o it. The S-S distance is 2-15 A.and the S-S-S angle 103”.The per-ions differ from the pyro-ions in that their oxygen atomsare joined, not shared. Zachariasen and his co-workersg3 havemade a careful study with Fourier analyses of the persulphate ionin the ammonium, potassium, arid caesium salts. The two SO,groups are joined somewhat askew (Fig. 4). The link between themis somewhat longer than the theorotical value 1.31, but the accuracyclaimed is $: 0.15 A.The ions Tl,Cl,”‘ 94 and WZCl9”’ 95 appear to be isomorphous,8g L. Pauling and J. Sherman, Proc. Nat. Acad. Xci., 1934,20,336.go J. Beintema, Proc. R. Alcud. Wetensch.Amsterdam, 1935, 38, 1015.91 2. Krist., 1935, 92, 190.g2 J . Chm. Physics, 1934, 2, 109; A., 1934, 479; 2. Krist., 1934, 89, 529.93 R. C. L. Mooney and W. H. Zachariasen, Physical Rev., 1933, [GI, 44,327 ;A., 1935, 152; 2. Krist., 1934, 88, 63; A., 1934, 1060; R. C. Keen, ibid., 1935,91, 129.94 J. L. Hoard and L. Goldstein, J. Chem. Physics, 1935, 3, 199; H. M.Powell and A. F. Wells, J., 1935, 1008.95 C. Brosset, Nature, 1935, 135, 874; Arkiv Kemi, Min. Qeol., 1935, 12,1441, 1220 CRYSTALLOURAPHY.with a pair of metal atoms surrounded by octahedra of chlorineatoms which share one face. Cs,As,CI, 96 does not, however, con-tain the ion As,CI,, but should be written (CsCl),(AsCI,),.The heteropoly-acids and their salts have been further investig-ated, particularly by J.F. Keggin,,' by X-ray powder methods.,*In combination, they behave as very large spherical ions, in theinterstices between which are found other ions and water molecules.It is interesting that the basicity of the different heteropoly-ionsis fixed by the number of positive ions that can fit in the invariablecalcium fluoride structure.Organo-metallic and Co-ordinate Ions.-The dimethylthalliumhalides are an isornorphous series of a layer lattice type. H. M.Powell and (Miss) D. Crowfoot 99 have shown that the H3C-T1-CH3group is linear, but also that the distance between neighbouringmethyl groups in neighbouring layers is 4.16 d., exactly the distancefound in methane but greater than that in durene, 3-81 A.Trimethylplatinum chloride is found by E.G. Cox and K. C.Webster to crystallise in the cubic system and to have a trigonalaxis of symmetry. The four platinum valencies for this type ofbinding cannot be coplanar. Diamminosilver groups inare probably linear, and the Cd(NH,), groups in CC~(NH,),(R~O,)~are tetrahedral.A large number of workers have been concerned t o show by X-raymethods whether the4-co-ordination compounds of nickel, palladium,platinum, and copper are tetrahedral or planar ; except the trimethylcompound, all are found to be planar. The clearest structure is thatof [Pd(NH,)4]C1,,H20, studied by B. N. Dickinson.6 The Pd(NH,),groups lie in planes 4.3 A. apart, which are separated by chlorine ionswith the water groups in the interstices of the structure.The Pd-Ndistance is found to be 2.02 A. and the group is strictly tetragonal.An elaborate study has been made of (NH4),CuC1,,2H,0 by 1,.Chrobak to clear up disputes that had existed as to its nature.s6 J. L. Hoard and L. Goldstein, J. Chem. Physics, 1935, 3, 117.9 7 Proc. Roy. SOC., 1934, [A], 144, 75; A., 1934, 479; see also J. D. H.Donnay and J. MBlon, Proc. Nat. Acad. Sci., 1934, 20, 327; A., 1934, 947;J. W. Illingworth and J. F. Keggin, J., 1935, 575; A., 834; J. A. Santos,Proc. Bog. SOC., 1936, [A], 150, 309; 0. Kraus, 2. Krist., 1935, 91, 402.ss See Ann. Raports, 1933, 30,409.1 Ibid., 1935, 90, 561.2. Krist., 1934, 8'9, 370; A., 1934, 479.R. B. Corey and R. W. G. Wyckoff, ibid., 1934,87,264; A., 1934, 352.R.B. Corey and K. Petrescov, &id., 1935, 89, 528.K. S. Piker, ibid., 92, 131.5 Ibid., 1934, $8, 281; A., 1934, 1161. Ibid., p. 36; A , , 1934, 1060BERNAL AND WELLS : CRYSTAL CHEMISTRY. 221A planar arrangement is found for the four chlorine atoms, thoughthey turn out to be at different distcznces-2.0 and 2.35 A.-from thecopper atom. The water molecules here are, however, co-ordinatedat a distance of 2-0 A. from the copper. E. G. Cox, W. Wardlaw, andK. C. Webster 7 have studied a number of other complex derivativesof palladium, platinum, nickel and copper. The most convincingevidence is obtained from the dithio-oxalate derivatives of thefirst three metals, which crystallise with the whole of the complexin planes separated by a distance of 5.5 A.apart and havediad axes of symmetry. Similar evidence is provided by salicyl-aldoxime and other complexes of these metals, all of which crystallisewith the complex molecules in layers 4 A. apart, excluding anypossibility of tetrahedral arrangement.Similar results have been found for palladium chloride, oxalate,and chloro-dinitrite,8 but is was impossible to analyse the simplecompound PdC12(NHJ2 on account of its forming a two-dimensionallattice of a statistical kind (see p. 188).A study showing a complete isomorphism between the tetra-cyanide salts of nickel, palladium, and platinum and one less com-plete between those of Mg, V and Er has been made by H. Brasseurand his collaborator^.^ The complex has a centre of symmetry andtherefore must have a planar configuration. On the other hand, inCs3CoC1, studied by H.M. Powell and A, F. Wells lo the complexCoCl, seems to exist as a regular tetrahedron, the remaining C1ion occupying a different place in the structure.Of the hexa-co-ordinated compounds an interesting example isgiven by [Rh(NH3)5C1]C12.11 The complex ions are slightly distortedoctahedra, held together by the free chlorine ions. Nickel nitrites l2and caesium aurichlorides l3 have also been studied.Hydrated 8uZts.Recent detailed studies of hydrated salts havebrought out the function of water of crystallisation much moreclearly. Water is found, in general, either attached to a positive7 J., 1935,731,1475; see also F. W. Pinlcard, E. Sharratt, W. Wardlaw, and(in part) E.G. Cox, J., 1934,1012; A., 1934,994; E. 0;. Cox, H. Saenger, andW. Wardlaw, ibid., p. 182; A., 1934, 397.F. G. Mann, (Miss) D. M. Crowfoot, D. C. Gattiker, and (Mrs.) N. Wooster,J., 1935, 1642.a J. Pi6rard and A. de Rassenfosse, 2. Krist., 1935, 90, 470; A. de Rassen-fosse and J. PiBrard, Bull. SOC. Sci. LiBge, 1935, 74; H. Brasseur and A. deRassenfosse, ibid., pp. 24, 68,171, 277 ; H. Brasseur, A. de Rassenfosse, and J.Pidrard, Compt. rend., 1934,198, 1048; A., 1934, 479.10 J., 1935, 359.11 C. D. West, Z. Krist., 1935, 91, 181.12 A. Ferrari and C. Colla, Qazzetta, 1935, 65, 168, 789, 809; A. Ferrari, A.13 N. Elliott, J . Chem. Physics, 1934, 2, 419 ; A., 1934, 947.Baroni, and C. Colla, ibid., p. 797222 CRYSTALLOGRAPHY.ion, or lying between other water molecules and negative ions.Ineither case the arrangement of the water molecule is such as to satisfythe binding properties postulated by the Bernal-Fowler theory.14In the first case the ion may occupy one or two of the positions ofnegative attraction in the molecule ion, according to its polarisingpower. The degree of binding of the water is shown very clearly byits infra-red absorption,l5 which varies from that of ice to that ofwater according to the tightness with which the molecule is held.Lithium sulphide monohydrate is the only example of a monohydr-ate studied.l6 Each water molecule is attached to one lithium atom,to two sulphate oxygens, and to another water molecule. Thebinding is so slight, M,O-H,O = 2.86 A., that rotation of groups isnot excluded. The crystal structure of CuS04,SH,0, which has beencompletely worked out by C.A. Beevers and H. Lipson,17 is ofparticular interest to chemists. The five water molecules are differ-ently situated ; four are arranged in a plane about the copper atomsat a distance of 1.97-2-0 &, and the other is not attached to anymetal atom but connected tetrahedrally to two water molecules ofthe first type and two sulphate oxygens. The copper group alsocontains two sulphate oxygens, but at a greater distance, 2.3,2-45 8., so there is no doubt that water molecules are here held byplanar co-ordination forces. The whole structure satisfies veryexactly Pauling's ionic valency scheme. C. A. Beevers and C. M.Schwartz l8 have examined NiS04,7H,0, and here again six of thewater molecules are co-ordinated to the nickel and one is loose.In the hexahydrates of magnesium and aluminium halides, analmost regular octahedral co-ordination of water molecules roundthe cations is found.lg Some curious isomorphous relations havebeen found by C.D. West 2o in the hydrates of perchlorates andiodides. In the first place, iodine and perchlorate ions seem tofunction almost identically in the structure owing to high symmetry,not to rotation. In the second place, Ba(C10,),,3H20 is foundto be isomorphous with LiC104,3H,0.A very complete study of the alums M1I16H2O,MI( S04),GH,0 hasbeen made by H. Lipson.21 Three types of alum structure have beenl4 See Ann. Reports, 1934, 31, 42.15 L.Passerini, Gazzetta, 1935, 65, 502, 511 ; A., 1300.16 G. E. Ziegler, 2. Krist., 1934, 89, 456.1' Nature, 1934,133,214; A., 1934,243 ; Proc. Roy. SOC., 1934, [A], 146,570.la 2. Krist., 1935, 91, 157.K. R. Andreas and J. Gundermann, ibid., 1934, 87, 345; A., 1934, 479;K. R. Andress and C. Carpenter, ibid., p. 446 ; A., 1934,947.20 Ibid., 88, 198; A., 1934, 1161; ibid., 1935, 91, 480.21 Phil. Mag., 1935,19,887; PTOC. Roy. SOC., 1935, [A], 151,347; A., 1308;H. Lipson and C. A. Beevers, ibid., 148, 664CROWFOOT : MOLECULAR CRYSTfiS. 223found, corresponding to (i) verylarge univalent ions, e.g.,Cs,N(CH,), ;(ii) medium-sized ions, Rb,K; and (iii) small ions, Na. All alumshave in common the co-ordination of six water molecules round thetervalent cation.The first two differ in the arrangement of theremaining six water molecules, and sodium alum has the reverseposition of the sulphate group along the trigonal axis. As all threeare cubic structures, we have here a case where only X-rays canshow that the series is not isomorphous.The only complete study of a salt containing molecules, otherthan water and ammonia, has been made by S. B. Hendricks forCaS04,4CO(NH2)2.22 The urea groups act as dipole links betweenthe positive and negative ions of the salt. AgN03,CO(NH2), hasprobably a similar structure.23 J. D. B.A. F. W.MOLECULAR CRYSTALS.Last year some of the most important advances described in thereport were those resulting from the application of rapid preliminarymeasurements and extensive surveys of related substances to thestructure of unknown chemical compounds.Such was the workon the sterols, sex hormones, and related compounds which hascontinued to yield valuable results. This method depends upon theuse of optical or magnetic measurements to determine the probableorientation of the molecules in the crystal, and upon the use ofmolecular models derived from the results of exact structure deter-minations.Considerable doubt has been expressed in the past as to theabsolute reliability of the first of ilhese methods, and it is thereforeparticularly satisfactory that we now have several examples in whichexact structure determinations have confirmed the molecular orient-ations chosen from optical and magnetic data.2 Further, a verycomplete test has been applied to the whole theory by S.B. Hen-dricks and W. E. Derning3 from an examination of the opticalanisotropy of the crystals of a series of oxalates. They have22 J . Physical Chem., 1933, 37, 1109; A., 1934, 243.23 G. L. Clark and C. 0. Werner, 2. Krist., 1934, $8, 162; A., 1934, 1162.1 G. E. R. Schulze, 2. physikal. Chem., 1934, [A], 171, 436; Y. Go and 0.Kratky, ibid., [B], 26,439 ; J. D. Bernal and (Miss) D. M. Crowfoot, Chem. andId., 1934,53,953; A., 1934, 1354; 1935,54,701; A., 1120; D. M. Crowfoot,ibid., p. 568; A. Kofler and A. Hauschild, 2. physiol. Chem., 1934, 224, 150;A., 1934, 815; S . B. Hendricks, 2. Krist., 1934, $9, 427; A,, 1935, 152; A.Neuhaus, ibid., 89, 505; A., 1934, 413; ibid., 1935, 9Q, 415; A., 1195; H.Brasseur, ibid., 91, 369; G.Mackinney, J . Arner. Chem. SOC., 1934, 58, 488;A., 1934, 352.2 K. S. Krishnan and S. Banerjee, Proc. Roy. Soc., 1935, 234,265.3 2. Krist., 1935, 91, 290224 CRYSTALLOGRAPHY.calculated the birefringences of the crystals from the molecularrefractivities and the orientations of the molecules in the crystalpreviously deduced from X-ray data. There is very close agreementbetween the calculated and observed birefringences, which indicatesthat no confusion is caused by intermolecular interaction. Similarcalculations have been made with good results for guanidiniumiodide and for sodium carbonate rnon~hydrate.~ The usefulnessof even the molecular refractivities calculated direct from the crystalrefractive indices as an indication of molecular structure has beendemonstrated by A.Neuhaus for a large series of compounds.Still more important advances have been made in the directionof exact structure determination, and it is in this field that we havemost interesting results to report. Last year we listed the inter-atomic distances found in seven organic crystals of which completestructure analyses had been made up to that date, but this listcould now be more than doubled. A very good summary of theextent to which interatomic distances had been measured withprecision by X-rays up to the end of 1934 has been given by J. M.Robertson.' Another list also appears in a paper by H. Markwhich supplies in addition a valuable survey of the various physicalmethods available for the study of the shape and structure oforganic molecules.The first Fourier analyscs of organic compounds, such as those ofurea, thiourea, naphthalene, and anthracene, did little more thanrender precise the pictures of the structures already accepted byorganic chemists through the attachment of these exact interatomicdistances.But the last two years have seen the extension of themethod into the field of pure chemistry in two directions. Thefirst is the direct determination of the mutual orientation of theconstituent atoms where this is unknown, as in the case of cyanurictriazide (see below). The second is a determination of the nature ofthe chemical bonds present. The measurements of standardorganic compounds have provided us with a scale of bond lengths,normal distances between atoms both inter- and intra-molecular, tobe applied to actual substances under investigation. But the resultsobtained by the application of this scale are rapidly leading usbeyond the pictures of molecular structure given us by classicalorganic chemistry.Simple Molecular Structures ,-Considerable work has been doneby improved techniques in the examination of crystals at lowH.Brasseur, ibid., p. 282. 4 W. Theilacker, 2. Krist., 1935, 91, 90.6 Ber., 1934, 67, 1627.7 Phys. SOC. Rep., p. 46; Chem. Rev., 1935,16, 417.3 2. Elektrochem., 1934,40,413; A., 1934, 1088CROWFOOT : MOLECULAR CRYSTALS. 225temperatures. L. Vegard has determined the structures ofa-(fixed) and P-(rotating) nitrogen, and shown that those of carbonmonoxide are almost exactly similar.10 The C-0 distance in solidcarbon dioxide is found to be 1.13 -J= 0.02A.11 The structure ofoxygen in its different forms has been very much studied, but noconclusive results have been obtained.Absorption-spectrumstudies l2 point to the existence of O4 molecules in liquid oxygen andin all forms of solid oxygen. Vegard l3 has shown that y (high-temperature) oxygen has a cubic structure a = 6-83 A. containing16 atoms and consequently almost certainly four rotating moleculesof 0,. These must lie alongstructure such as (I) is more0(1.1 00 0have very similar structures,the trigonal axes, and consequently aprobable than (11); a- and p-oxygen(11.)0-00-0but they are rhombohedra1 and notcubic and contain three molecules of 0,.E.F. Burton and W. F. Oliver l4 have shown that water vapourFIG. 5.Molecule of Sulphur S,.condensed a t temperatures below -- 110" gives rise, not to ice, butto water glass, which, to judge from the position of the intensitymaxima, must have a density equal to or less than that of ice a t thesame temperature. At - 110" this water glass rapidly devitrifies toordinary ice. Solid hydrogen peroxide l5 is found to have a tetra-gonal structure, c = 8-02, a = 4.02, with four molecules per cell.The arrangement may be similar to that of cristobalite.The structure of two forms of sulphur has been determined.A careful study of rhombic sulphur by A.E. Warren and J. T.Burwell l6 has shown that the cell contains 16 molecules of S8;these molecules are in the form of puckered octagons (see Fig. 5),9 Proc. K. Alcad. Wetensch. Amsterdam, 1934, 37, 780; A., 1935, 147.10 2. Physik, 1934, 88, 235; A., 1934, 587.11 W. H. Keesom and J. W. L. Kohler, Physicu, 1934, 1, 167; A., 1934, 244.12 A. Prichotko, M. Ruhemann, and A. Federitenko, Physikul. 2. Sovietuniora,1935, 7, 410; A., 1291; M. Guillien, Compt. rend., 1934, 198, 1456; A., 1934,581 ; H. Salow, 2. Physik, 1934,90,11; A., 1934,1055; W. Finkelnburg, ibid.,p. 1 ; A., 1934, 1055.13 Ibid., 1935, 98, 1.15 F. Feher and F. Klotzer, 2. Elektrochem., 1935, 41, 850.1 6 J . Chem. Physics, 1935, 3, 6.l4 Proc. Roy. SOC., 1935, [ A ] , 153, 166.REP.-VOL.XXXII. 226 CRYSTALLOGRAPHY.with an S-S distance of 2.12 A. (calc., 2.16) and a bond angle of105.4". The S8 molecules are stacked in four layers approximatelyperpendicular alternately to the (110) and (1x0) directions in thecell ; the nearest approach between sulphur atoms in neighbouringmolecules is 3.3 A. Plastic sulphur is the simplest type of poly-merised fibre structure. On stretching, it can, like rubber, bemade to crystallise, though normally it is amorphous: that is,the sulphur chains are tangled with each other. The structurethat these fibres form has been thoroughly worked out by K. H.Meyer and Y. Go;17 the cell is monoclinic with an identity periodof 9.26 8. along the fibre axis. A close analogy to the polymorphismof sulphur is furnished by (PCl,N), which forms both 3- and 6-unitrings18 and also elastic polymerised fibres of period 5.16 Partialstudies have been made of two red monoclinic varieties of selenium 2owhich also probably contain Se8 molecules.The structure of red and black phosphorus has been studied byR.Hultgren, N. S. Gingrich, and B. E. Warren.21 The amorphousform of both has been analysed and shows a layer lattice of 3-co-ordination type not unlike that of graphite with an internucleardistance of 2.28B. The crystalline form, on the other hand, is anew type of structure and, like arsenic, of the layer type, with3-co-ordination but with a rhombic type of trigonal layers. Theatoms in the layers are 2.188. apart (calc., 2.20A.). The atomsin different layers are separated by 3.68 A.Molecules of the symmetrical types AB,, AB,, generally formsimple crystal structures.Exceptions to this rule are ZrF4 andHfF, which give monoclinic crystals.22 Pentaerythritol tetra-phenyl ether, on the other hand, has a simple tetragonal cell witha = 12.32, c = 8-43 A., with alternating tetragonal symmetry andtwo molecules in the unit cell.23 This is very similar to tetraphenyl-methaneY2, which is also tetragonal, a = 10.86, c = 7.26 B.,differing only in the smaller axes and in the fact that here the mole-cule also possesses planes of symmetry. Hexamethylethane andhexachloroethane,25 above - 125" and 71" respectively, are cubic17 Helv. Chim. Acta, 1934, 1'7, 1081.l8 I?. Renaud, Ann. Chirn., 1935, [xi], 3, 443; A., 833; Cornpt.rend., 1934,19 Arch. Sci. phys. nat., 1935,17, supp. 139; Trans. Paraday SOC., 1936, 32,30 H. P. Klug, 2. Krist., 1934, 88, 128; A,, 1934, 1160.21 J . Chem. Physics, 1935, 3, 351.22 G. E. Schulze, 2. Krist., 1934, 89, 477.23 J. Beintema, P. Terpstm, and W. J. van Weerden, Rec. trav. chim., 1935,e4 W. H. George, Proc. Roy. Soc., 1926, [A], 113, 585.25 C. D. West, 2. Krist., 1934, 88, 195; A., 1934, 1162.198,1159; A., 1934, 615.148.44,627 ; A., 1195CROWFOOT : MOLECULAR CRYSTALS. 227body-centred structures, again with only two molecules in the cell,due presumably to molecular rotation. Of the less symmetricaldisubstituted ethane derivatives, s-di-iodoethane 26 shows a consider-ably more complicated packing. The molecules do not rotate aboutthe C-C bond a t ordinary temperatures, and it is interesting that theposition taken up by the iodine atoms with respect to one anotheris the same as that in s-di-iodoethylene, vix., the trans-position.The crystals of these two compounds are very closely isomorphous.Aliphatic Compounds.-Among the main group of aliphatic com-pounds exact structure determinations are still very rare.We havestill no Fourier analysis of aliphatic long chains, though a beginninghas been made by D. A. Wilson and E. Ott 27 towards the calculationof the intensities of the main plane reflexions of a series of aliphaticalcohols. Otherwise, work in this field is mainly confined in useful-ness to the identification of products from natural sources 28together with preliminary studies on the structure of dibasic acids,29trigly~erides,~O and dihydrazides .31 I n the series of the poly-methylene ring compounds 32 the interesting fact emerges that,whereas a t ordinary temperatures and in the liquid the molecularvolume of a methylene group is greater in the cyclic than in thestraight-chain compounds, yet this difference disappears a t lowtemperatures.The only complete structure determinations in the aliphaticseries are those of hexamethylenetetramine and urea, which havebeen further refined by R.W. G. Wyckoff and R. B. C ~ r e y . ~ ~ Theirresults give valuable new readings for the P curves of carbon andnitrogen in this type of compound, and also lead to slightly differentvalues for the interatomic distances.In hexamethylenetetramine,CH,-N = 1.42 A., while in urea, C-=O = 1.25 and C-NH, = 1-37 A.The shortening of the distance of C-N in urea from 1-42 to 1.37 8.is of particular interest, since here resonance may occur betweenthe two forms H2N>Cx0 and HN>C-OH, the former pre-dominating.H2N H P26 H.P. Klug, J . Chem. Physics, 1935,3,747; 2. Krist., 1935,90,495; A., 1195.2 7 J. Chem. Physics, 1934, 2, 231, 239; A., 1934, 720.28 F. J. E. Collins, J . SOC. Chem. Inti., 1935, 54, 33; S. H. Piper, A. C.Chibnall, and E. F. Williams, Biochem. J., 1934, 28, 2175; A. C. Chibnall,S. H. Piper, A. Pollard, E. F. Williams, rtnd P. N. Sahai, ibid., p. 2189; A. C.Chibnall and S . H. Piper, ibid., p. 2209; A., 1935, 551, 152, 267, 204.29 F.D. La, Tour and A. Riedberger, Compt. rend., 1934, 199, 215; A.,1934, 1060; F. D. La Tour, ibid., 1935,201,479; A., 1351.30 C. E. Clarkson and T. Malkin, J., 1934, 666; A., 1934, 720.31 M. Wolf, Physica, 1934, 1, 417; A., 1934, 587.32 A. Miiller, Nature, 1935, 135, 994 ; A ., 957.33 Z. Krist., 1934,89, 462; cf. R. Reinicke, ibid., 1935, 87,417228 CRYSTALLOGRAPHY.In the guanidinium halides investigated by W. TheilackerF4the distance C-N is still more reduced, the value given being 1-18 a.,although the measurement is not susceptible of great accuracy.Theilacker has studied the chloride, bromide, and iodide, but onlyfor the last could the crystal structure be determined with anyapproach to precision. This forms a typical layer lattice withiodine ions arranged on a network of puckered hexagonal ringsseparated by guanidine ions.The guanidinium ion C(NH2),shows trigonal symmetry, all three nitrogen atoms being crystal-lographically equivalent, and the ionic character cannot thereforeFIG. 6. FIG. 7.Carbon. 0 Oxygen.The. oxalate-ion.4 O Nitrogen.The molecule Be40(CH,*COO) (one acetate groupbe associated with any particular nitrogen atom of the complex.The structure may be written as (I) with a positive charge on thei s omitted).NH2carbon, or as due to resonance between three double- bondedstructures of the type (11).Considerable interest has centred round another " resonance "problem, wuiz., the structure of the carboxyl group, and severalstudies have been made of carboxylic acids and their salts.35 Besidess4 2.Krist., 1935, 90, 51, 256; cf. A. Swaryczewski, Bull. Acad. polonaise,1933, [A], 359; A., 1934, 587; ibid., 1934, [A], 246; A., 1935, 152.35 L. P. Biefield and P. M. Harris, J . Amer. Chem. SOC., 1935, 57, 396; E.Hertel and G. X I . Romer, 2. physilcal. Chem., 1934, CB], 27 282; A., 1935, 152;R. C. Evans, 2. Krist., 1935, 92, 154CROWFOOT : MOLECULAR CRYSTALS. 229the electron diffraction of formic alcid 36 reported last year, Paulinghas examined the crystal structure of basic beryllium acetate.37Here he finds actual molecules Be,O(CEI,*COO), present in thecrystal and packed together as are the atoms in diamond. Insidethe molecules (Fig. 6) each beryllium atom is a t the centre of atetrahedron formed by three oxygen atoms contributed by acetategroups and the central basic oxygen.The interatomic distanceshave not been determined with any great accuracy, but Pauling candetect, as in formic acid, no difference between the two oxygen atomsof the carboxyl group. He gives the C-0 distance as 1.29 0-058. and the 0-C-0 angle as 124" & 3".A somewhat more exact determination of the configuration ofthe carboxyl group has been made by W. H. Zachariasen38 in hisanalysis of the structure of oxalic acid dihydrate, and this has beenconfirmed by S. B. Hendricks for other o x a l a t e ~ . ~ ~ Zachariasenfinds for the oxalate group a planar configuration with a centre ofsymmetry (Fig. 7). The C-C distance is 1-59 & 0.07&, C-0 inboth cases 1-25 0.05 A., and the 0--GO angle 126".The two oxygenatoms are not, however, structurally identical, and their arrangementwith respect to the water molecules in the crystal is different.Since the distances between the oxygen atoms in the oxalate groupsand water molecules are only 2.87, 2-77, and 2-60 8., considerablyshorter than the usual intramolecular distance of 3.5 k, Zachariasenhas suggested that the water molecules bind the oxalate groups inchains by a series of hydrogen bonds. Later, J. D. Bernal and(Miss) H, D. Megaw 40 showed that there are two possible ways ofachieving this binding through two different systems of combinedhydrogen and hydroxyl bonds according to whether 0, or 0, isacting as hydroxyl group.The interconversion of the two systems iseffected by the movement of hydrogen atoms along the oxygenchains, and this movement provides a mechanism for the resonanceof the two forms :It does seem, however, that resonance may not be complete, and thelimits of error of Zachariasen's measurement leave still open thepossibility of comparatively small differences in the C-0, andC - 0 , distances.Aromatic Cmpounds.-In the aromatic series a number of new3G L. Pauling and L. 0. Brockway, Proc. Nat. Acad. Sci., 1934,20, 336.37 L. Pauling and J. Sherman, ibid., p. 340.38 2. Krist., 1934, 89, 442; A., 1935, 152; Physical Rev., 1934, 45, 755.39 2. Krist., 1935, 91, 48.4 O PTOC. ROY. A'Yoc., 1935, [ A ] , 151, 384230 CRY STALLOQRAPHP.and very important structure analyses have been carried out.Thesimplest of these is resorcin01,~~ of which only a preliminary reportis available. Here the benzene ring appears regular, with a C-Cdistance 1.41 A,, and C-OH 1-35 A. The molecules are arrangedin spiral formation about the diad screw axis in such a way thathydroxyl groups in neighbouring molecules are brought to within adistance of 2.66-2.76A. of one another. This close approachindicates binding between the hydroxyl groups of the kind discussedabove with reference to oxalic acid and also among inorganic com-pounds. Such association between hydroxyl groups has long beenrecognised in organic chemistry, but these measurements providethe first accurate description of the nature of the binding.Research has been continued on several compounds based oncondensed ring systems.The complete analysis of chrysene42 isof particular interest as a control to the work undertaken on hydro-carbons related to the sterols.43 Preliminary measurements areF I ~ . 8.Dibenzyl.also reported for 1 : 2-cyclopentenophenanthrene 44 and for dodeca-hydrobenzanthracene 45 which shows, as would be expected, aconsiderable thickening of the molecule, and also of the optical andmagnetic properties of 1 : 2 : 5 : 6-dibenzanthracenej6 1 : 3 : 5-Triphenylbenzene 47 is closely related in crystallographic behaviourto the condensed-ring compounds, since the molecules appearperfectly flat with all the phenyl rings extended symmetricallycoplanar with the central ring.In the crystals, they are packedclosely interlocking in layers, with the molecular planes very slightlyinclined to the normal to a pseudotrigonal axis.4 1 J. M. Robertson, 2. Krist., 1934, 89, 318; Nature, 1935,136, 755.4 2 J. Iball, Proc. Roy. SOC., 1934, [A], 146, 140; A,, 1934, 1162.4 3 J. D. Bernal and (Miss) D. M. Crowfoot, J . , 1935, 93.44 J. Iball, 2. Krist., 1935, 92, 293.4 5 Idem, Chem. and I d . , 1935,54, 716.4 G J. Iball and J. M. Robertson, Nature, 1933,132,750; A., 1934, 17; J. D.13erna1, ibid., p. 751; A., 1934, 18; K. S. Krishnan and S. Banerjee, 2. Krist.,1935, 91, 170, 173.4 7 B. P. Orelkin, J . Ben. Chem. Russia, 1933,3, 643; A., 1934, 134; (Mrs.)K. Lonsdale, Nature, 1934, 133, 67; A., 1934, 134; B. Orelkin and (Mrs.) K.Lonsdale, Proc.Roy. Soc., 1934, [ A ] , 144,630; A., 1934, 834; K. S . Krishnanand S. Banerjee, Nature, 1934,133, 497 ; A., 1934, 479CROWFOOT : MOLECULAR CRYSTALS. 231In dibenzyl, on the other hand, in contrast with the arrangementin triphenylbenzene and also in diphenyl, the two benzene rings areno longer coplanar. Preliminary examination by J. Dhar 48suggested a molecule only slightly distorted from the coplanarstructure, but the complete analysis by J. M. Robertson49 showsclearly that the planes of the benzene rings are directly at right anglest o the zigzag of the CH, groups (Fig. 8). Between the aliphaticand aromatic carbon atoms the distance is 1.47 A., and between thetwo CH, groups it is 1.58 A. The angle between the bonds of theCH, groups is 109*2-112".In all the compounds so far considered, the benzene rings appearas perfectly regular hexagons with a distance between the carbonatoms of 1.41 A.In benzoquinone, chemical theory would expectconsiderable distortion from this model, and this has been found tobe the ~ase.~O Owing to the orientation of the molecules in thecrystal, their dimensions cannot be obtained from the FourierFIU. 9.Benzoqu!inone.analysis with such accuracy as in other examples. But there doesappear to be definite lengthening of the C-C bonds adjacent to the(2x0 group to 1.50b., and shortening of the ring bonds parallelto this to 1-32b., corresponding to the appearance of aliphaticsingle and double bonds (Fig. 9). The C=O distance appearssmaller than might be expected, 1*14A., but this agrees with theC=O distance of 1.16 A.found in carbon dioxide from the infra-redabsorption spectrum and 1.13 A. from crystal-structure data atlow temperatures (p. 225). It may be compared with the C=Qdistance of 1-25 A. found for urea and oxalic acid, and in so far, itconfirms that the latter are midway between ' true ' single anddouble bonds.This distortion of the benzoquinone molecule is, a t least in itsdirection, in accordance with current chemical theory. But nearlyas far-reaching changes of an altogether unexpected kind have48 Current Sci., 1934, 2, 480; A., 1934, 948.4 9 Proc. Roy. SOC., 1934, 146, 473; 1935, 150, 348.60 Ibid., p. 106; Nature, 1934,134, 138; A., 1934, 948232 CRYSTALLOGRAPHY.been found by R.W. James, G. King, and H. Horrocks in p-dinitro-ben~ene.~l A preliminary examination of this compound, carriedout by I<. Banerjee,52 gave results roughly in agreement with thestereochemical picture presented by the ordinary chemical formula.The exact structure obtained by James by Fourier projections onthree planes reveals important departures from this picture whichare best shown by reference to Fig. 10. The molecule as a wholepossesses a centre of symmetry. The nitro-group is nearly planar,but apparently not quite, and nearly coplanar with the benzenering, one oxygen atom being in this plane and the second slightlylifted above it. The distance between the carbon atom of thering and the nitrogen atom is 1-53,&., decidedly longer than theC-N distance of hexamethylenetetramine.Further, the two oxygenatoms are at different distances from the nitrogen, vix., 1-10 andFIG. 10.p -Dindrobenzene.1.25A.N+O in the usually written structure of the nitro-group -Nfthough both are actually shorter than the accepted distances,uuix., for N=O, 1.22 A., and for N+O, 1.36 It is surprising,however, that any difference should exist between them at all,since the resonance energy between the two equivalent configurationsis considerable. Very careful measurements by H. 0. Jenkins 54have shown that p-dinitrobenzene has no dipole moment, and thishas been taken to prove that the oxygen atoms of the nitro-group areequivalent. The only alternative is to assume that the exact con-figuration shown to exist in the solid state, which has a centre ofThese might correspond to distances between N=O and\O?51 Proc.Roy. SOC., 1935, 153, 225.62 Phil. Mag., 1934, 18, 1004.53 N. V. Sidgwick, Ann. Reports, 1934,31, 39.54 Nature, 1934, 134, 217CROWFOOT : MOL'ECULAR CRYSTALS. 233symmetry, is also that present in solution, i.e., that there is no freerotation about the C-N bond.Perhaps one fact in support of this hypothesis is the very markedinteraction that appears to occur between the nitro-group and thebenzene nucleus. The substitution of the nitro-group has produceda considerable shortening of one of the bonds in the ring adjacentto it-that approximately parallel to the shorter N=O bond-though there is no compensatory lengthening of other nuclear bonds.The configuration of the ring as a whole can be regarded as tendingtowards one of the Dewar types of canonical structure which inFIG.11.Cyanuric triazide.benzene itself is probably only present to the extent of about 703%(Pauling and Wheland).55 But we have evidently t o deal here witha process which it is practically impossible to discuss in terms ofordinary valency changes. It would be most interesting if thisstriking modification in shape of the benzene nucleus produced bythe substitution in it of nitro-groups could be related to the generalphenomenon of the influence of substituents on the reactivity of thebenzene nucleus.More information in the same direction is given by the determin-ation of the crystal structure of cyanuric triazide, one of the most im-portant and elegant pieces of work accomplished in the last two years.B G J.Chem. Physics, 3933, 1, 362.H 234 CRYSTALLOGRAPHY.Two parallel investigations have been undertaken. That of E. A.Hughes 56 leads to a structure agreeing within the limits of his ownexperimental accuracy with that of (Miss) I. KnaggsY57 although itmakes no pretensions to such perfection. It is, however, of someinterest in indicating how far merely visual estimates of intensitiesmay be relied on to give a very good first approximation picture ofa complex structure. Miss Knaggs has made very accurate intensitymeasurements and converted these into an absolute scale bycomparison with standard crystals both by ionisation and photo-graphic methods. The results of her analysis lead to the structureof the cyanuric triazide molecule shown in Fig.11. The moleciileas a whole is planar, with a trigonal axis perpendicular to the plane.The azide group is attached to the carbon atom of the ring and isproved to be linear, the possible deviation from the straight line beingnot more than 4". It is, however, not centrosymmetrical, thedistance between the nitrogen attached to the ring and the centralnitrogen atom being 1*26A., while that between the two outernitrogen atoms is 1.11 A. This is in good agreement with thesuggestion of N. V. Sidgwick 58 that the actual structure is the resultof resonance between -N=NTIU and -N+-N?N.The ring itself is considerably distorted from the hexagonalshape.It consists of alternate carbon and nitrogen atoms whosedistances are alternately 1.31 and 1.39 8. apart. Both thesedistances are shorter than C-N of hexamethylenetetramine, but asa first approximation they may be attributed to alternate doubleand single links. We must assume that, in contrast to benzeneitself, one of the two Kekulk forms is frozen in cyanuric triazide bythe unsymmetrical form of the azide substituent, just as in p-dinitro-benzene another of the canonical structures appears forced on themolecule.A number of other investigations of aromatic compounds arestill in a preliminary stage.59 That of W. -a. Taylor on methylene-blue halides 6o is interesting in showing that the packing of organicions in a crystal follows much the same principles as that of inorganic66 J .Chem. Physics, 1935, 3, 1, 650.5 7 Proc. Roy. SOC., 1935, [A], 150, 576; A., 1194; Nature, 1935, 135, 268;6 8 Trans. Paraday SOC., 1934, 30, 801.59 R. G. Wood, 8. H. Ayliffe, and N. M. Cullinane, Phil. Mag., 1935, [vii],19, 405; E. Hertel and E. Dumont, 2. physikul. Chem., 1935, [B], 29, 112;E. Hertel, ibid., p. 117; F. Wurstlin, 2. Krist., 1934, 88, 185; A., 1934, 1162;B. Gossner and H. Neff, ibid., 89,417; A., 1935, 152; J. Dhar and A. C. Guha,ibid., 1935, 91, 123; M. Prasad and P. H. Dalal, Current Sci., 1934, 3, 200;A . , 1935, 152; K. Banerjee and B. C. Guha, I n d i a n J . Physics, 1934, 9, 287.cf. (Sir) W. H. Bragg, ibid., 1934,134, 138; A., 1934, 948.Chew, and Id,, 1935, 54,732 ; 8.Kriat,, 1935,91,450 A,, 1295CROWFOOT : MOLECULAR CRYSTALS. 235ions. The iodide ion in methylene-blue iodide, for example, doesnot appear to be associated particularly with any special part ofthe C-N-S chain but is packed conveniently between the ends ofthe lath-shaped molecules. A still more complicated moleculartype is that of the phthalocyanines, where investigation proves thepresence of approximately square flat molecules having a centre ofsymmetry.6l This centre may be either left empty or occupied bythe metals nickel, copper, or platinum without distortion of thecrystal lattice, and in all these cases the four valencies of the metalsmust be coplanar.Carbohydrates.-The structure of the sugars is one of the mostdifficult problems to be attacked by the methods of X-ray crystal-lography. The shapes of the molecules depart very far from thesimple plane and linear varieties which have been dealt with alreadywith such success, and little or no help can be got from opticaldata to assist any intensive simple crystal analysis.X-Ray dataof a preliminary character have, however, continued to accumulate,both of simple mono-, di-, and tri-saccharides and their methyl,ncetyl, and other derivatives,62 and E. G. Cox, T. H. Goodwin, and(Miss) A. I. Wagstaff 63 have recently undertaken the review of theresults obtained from some sixty substances. The hardness,high melting point, and high densities of the crystals suggest thatthe crystal structure of the sugars is largely determined by thehydroxyl groups, which tend to interact to the greatest possibleextent and link the molecules together in all directions in the lattice.Any alteration in the groups attached to the ring, therefore, usuallyrequires a complete readjustment of the relative positions of thehydroxyl groups and hence of the molecules themselves.Thereis consequently very little relation a t first sight between the dimen-sions of unit cells of different compounds obtained by X-ray data.In the methylated sugars, however, the interactions betweenmolecules are greatly reduced, and here Cox has found it possibleto correlate directly the X-ray data with the shape and orientationof the molecule.The shape of the molecule must depend on the stereochemicalconfiguration of the pyranose ring on which it is based, and about61 J.M. Robertson, R. P. Linstead, and C. E. Dent, Nature, 1935,135,506 ;J. M. Robertson, J., 1935, 615.62 H. Braekken, C. J. Koren, and N. i\. Sorensen, 2. Krist., 1934, 88, 205;A., 1934, 1162; G. Vavrinecz, Magyar Chem. Fol., 1933,39,40; A., 1934, 18;G. L. LeuckrtndH. Mark, J . Amer. Chem. SOC., 1934,56,1959; A., 1934, 1162;I(. Hess and K. Dziengel, Ber., 1935, 68, [B], 1594; A., 1226; C. Trogus andK. Hess, ibid., p. 1605; A., 1308; S. B. Hendriclcs, Nature, 1934, 133, 178;A., 1934, 241.63 J . , 1935, 978, 1498; A., 1195236 CRYSTALLOGRAPHY.this there has been considerable doubt. The most probablealternatives appear to be those drawn in Fig.12, either one of theSachse forms (cis and trans) found in cyclohexane derivatives orthe flat ring, previously discussed by Cox with reference to a-methyl-glucoside. In this ' flat ' ring the carbon atoms are probably inone plane, the oxygen slightly lifted out of it. In the Sachse ringsit is possible for hydroxyl groups t o be so attached that they lieeither directly in the ring or approximately at right angles to it,and this should lead to markedly different values for the thicknessFIG. 12.IH P@Carbon. 0 Oxygen.Possible conjiguration of the pyranose ring.to be observed for the molecules in the two cases. In the ' flat'ring no such distinction exists.Cox finds that the crystal structure of the methylated sugarsprovides a means for distinguishing the two cases.These tendto form long needles with an identity period along the needle axisin many cases of only about 4*5A.-too short a distance t o referto anything but the molecular thickness. Cox has collected 26examples of sugars in which one unit cell dimension is of this orderof magnitude, since such measurements give unequivocally avalue for the maximum size of the thickness. His results show thatthere is very little difference between the thicknesses measuredfor sugars having different configurations of the methoxyl groupsCROWFOOT : MOLECULAR CRYSTALS. 237For example, the maximum ' thickness ' found for a-lactose,4.69&, is very little greater than that of the three P-methyl-glucosides, 4.41-4-45 A. , and that of hexamethyl lyxosido-lyxosideis even smaller, 4.20 8.This therefore suggests that the ringstructure present is of the ' flat ' variety.Cox also finds certain very interesting examples of morpho-tropic relations between the crystal forms of related substances.The unit cell dimension of p-methylarabinoside, a-methylfucoside,and a-methylgalactoside 6-bromohydrin are given in the table.H CH, CH,BrHo 1-0, H Hyd-:>;H IGH H,lOH I-o H I@= =>I H 1-1 OMe H '1-1 OMe H 1-1 OMeH OH H OH H OH,8 -Methylarabinoside. a-Methylfucoside. 6 -bromohy drin.a -Methylgalac tosidedl00 8-10 9-96 10.58b 7.74 7.87 7.81C 5-89 5-72 2 x 5.62These inter-relations bear out the correctness of the configurationsassigned on chemical and optical properties to these three compounds,and also incidentally indicate the presence of the pyranose ring inor -methylfucoside.An exact knowledge of the configuration of the pyranose ringshould prove an important aid towards the complete solution ofthe structure of cellulose, the problem of which has recently beenreopened by M.mat hie^.^^ There is now a considerable accumul-ation of data on the reactions of cellulose and various derivative^.^^X-Ray measurements have also been made on chitin by K. H.Meyer and G . W. Pankow,g6 who find an arrangement of chitobioseunits in the unit cell closely related to cellulose. Starch micelles64 Compt. rend., 1934, 198, 1434; A., 1934, 587; Chim. et Ind., 1934, 31,Spec. No. 792; A,, 1934, 760; see also W. A. Sisson, Textile Res., 1935, 5,119; A., 1308; G.Champetier, Bull. SOC. chim., 1934, [v], 1, 613; A., 1934,993; J. Barsha and H. Hibbert, Canadian J . Res., 1934, 10, 170; A., 1934,515.6 5 C. Trogus and K. Hess, Cellulosechem., 1934, 15, 1 ; A., 1934, 244; Ber.,1935, 68, 1986; K. Hess, C. Trogus, and G. Abel, Cellulosechem., 1935, 16,79; A., 1356; K. Hess, C. Trogus, W. Eveking, E. Garthe, and N. Ljubitsch,Annalen, 1933, 506, 260, 295 ; 507, 62 ; A., 1933, 1280; K. Hess and M. U1-mann, Ber., 1934,67, [B], 2131 ; A., 1935, 201 ; J. J. Trillat, J . Chim. physique,1934, 31, 125; A., 1934, 479; M. Mathieu, Compt. rend., 1934, 199, 55; A.,1934, 956 ; C. Trogus and I(. Hess, 2. Elaktrochem., 1934,40,193 ; T. Tomonari,ibid., p. 207; A,, 1934, 637; M. Wadano, K.Hess, and C. Trogus, 2. physikalChem., 1935, [B], 30, 159, 170, 183; J. J. Trillat, J . Phys. Radium, 1934, [vii],5, 207; A., 1934, 834.6 6 Helv. Chim. A d a , 1935, 18, 589; A., 753238 CRYSTALLOGRAPHYhave been shown to be surrounded by a layer of water which isactually crystalline 67 and an attempt has also been made t o followthe various changes that occur in micellar structure during bread-making.G8 Other interesting observations are those on the mole-cular structure of sisal, coir, and and on pine t r a ~ h e i d s . ~ ~The photographs of coir, for example, show two patterns of cellulosechains crossed at 45" to one another, and in pine tracheids a singlespiral of cellulose is formed.The Structure of the Proteins.-Since, on present chemical theory,the proteins are built of amino-acids united by peptide links, oneobvious method of approaching the problem of their structure is tostudy the simpler synthetic polypeptides.K. H. Meyer andY. Go 71 have now made X-ray measurements of di-, tri-, tetra-,penta-, hexa-, and hepta-glycylglycine, and also of a polyglycyl-glycine of molecular weight about 2000 obtained from glycocollcarbonate. Unfortunately, only powder photographs could beobtained, but these show decreasing crystallinity in passing alongthe series, the photograph of heptaglycylglycine being very similarto those of the polyglycylglycine. From the tetrapeptide onwardsthe strongest spacings seem to be at 4-15 A. and 3.15 A,, with theformer finally dominating.This suggests a relatively simplearrangement of the chains in layers 4.2 A. apart.These photographs do not bear any very marked resemblancet o those which have been obtained from natural fibres such asfibroin and keratin.72 But this could hardly be expected, since inthe natural fibres the hydrogen of glycine is substituted by a numberof different groups-the R groups of the general formula. Thisproduces an anisotropy in the directions perpendicular to thefibre axis, which should be shown in the method of packing thechains in the fibres. It is with this theoretical possibility thatAstbury associates the two spacings observed in a great number ofsclero-proteins of 4.65 A. and 10-11 8. The first, the backbonespacing, is very constant in a large number of proteins.Thesecond, the side-chain spacing, varies somewhat from one species67 N. H. Kolkmeijer and J. C. L. Favejee, 2. Krist., 1934,88, 226; A., 1934,6s J. R. Katz and A. Weidinger, Z. physikal. Chem., 1934, 169, 321, 339;69 E. N. Miles Thomas and J. Hewitt, Nature, 1935,136,69; W. T. Astbury,70 R. D. Preston, Phil. Trans., 1935, [B], 224,131.71 Helv. Clzim. Acta, 1934, 17, 1488; A., 1935, 152.72 W. T. Astbury, Kolloid-Z., 1934, 69, 340; A., 1935, 162; F. Halle, i b a . ,p. 324; A., 1935, 162; W. T. Astbury and H. J. Woods, Phil. Trans,, 1933,[A], 232,333 ; A., 1934,352.1162.17'1,181; A., 1934,1070; 1935, 165.It. D. Preston, and A. G. Norman, ibid., p. 391 ; J. Hewitt, ibid., p. 647CROWFOOT MOLEC!ULAR CRYSTALS. 239to another, as would be expected with the varying nature of theR groups.Photographs taken of the fibres in the usual way aboutthe fibre axis show both spacings on the equatorial layer, and it isnot possible to determine their mutual orientation. Astbury has,however, discovered that orientation of the keratin crystallitescan be effected by lateral pressure in the presence of steam or hotwater.73 The keratin molecule is first transformed from thea-(contracted) to the @-(expanded) form by the pressure, and thecrystallites then turn so as to bring the ‘ side-chain’ spacingnormal to the plane of flattening. The backbone spacing provesto be very accurately at right angles to this. The observationsprovide strong confirmation for Astbury’s picture of the @-keratinstructure as one of extended polypeptide chains, the most markedperiodicity along the chain being one of 3-4 A.All the interconversion phenomena found between a- and @-keratin, including the transformation by pressure described above,have now been observed also with myosin, the protein of muscle.74Thus, myosin forms fibres which, on being roughly stretched parallel,show an X-ray photograph resembling that of a-keratin.On furfherstretching, the @-keratin photograph appears, which may be ‘ set ’by exposure to steam, but the fibres, like those of keratin, areelastic and, provided the fibre has not been stretched and dried, willcontract again.and the a -+ @-transformation, in particular, has been observed infrog’s sartorius muscle and the retractor muscle of the foot ofMytelw ed~lis.75~So far the polypeptide theory of protein structure very adequatelyaccounts for the simpler X-ray diffraction effects obtained from thescleroprotein fibres and films.It is more difficult at first sight t orelate such a structure to the properties of the soluble proteins.These behave in the ultracentrifuge as if built up of large, approxim-ately spherical molecules of molecular weight 35,000 or somemultiple of this, and the presence of molecules of this order ofmagnitude has now been proved also by the X-ray diffraction effectsobtained from crystalline pepsin and insulin. The early attemptsto obtain diffraction effects for crystalline proteins failed to showmore than two diffuse amorphous rings at about 10 and 4.3 A.-73 W.T. Astbury and W. A. Sisson, Proc. Roy. Soc., 1935, [A], 150, 533;A., 1195.74 W. T. Astbury and S. Dickinson, Nature, 1935,135, 95; A., 376.7 5 E. Saupe, Kolloid-Z., 1934, 69, 357; A., 1935, 231; A. Kiintzel and F.Pralike, Biochem. Z., 1933, 267, 243 ; A., 1934, 316 ; F, Worschitz, Fortschr.R6ntgemtrahlen, 1934, 50, 174; A., 1935, 1003; (with J. von Herman), ibid.,p. 178; A., 1935, 1021; H. Kolpak, Naturwiss., 1934, 22,, 72; A., 1934, 244,Other studies have been made on actual76a W. T. Aathury and S. Dickinson, Nature, 1935,135, 765; A., 772240 CRYSTALLOURAPHY.Astbury's side-chain and back-bone spacings respectively. These,from their appearance, had to be attributed to an amorphous ratherthan to a truly crystalline structure.The detection of the latterwas made possible by J. D. Bernal's observation 76 that most proteincrystals readily lose water on exposure to the air, so that the crystalsits usually examined were only pseudomorphs. By taking photo-graphs of crystals of pepsin immersed in the mother-liquor, he wasable to obtain a true crystalline diffraction pattern, and thisprocedure has since been followed for a number of other proteins,e.y., haemoglobin, edestin, and e~celsin.'~ Imperfect powder photo-graphs of urease and pepsin had previously been obtained by I.Fanku~hen.7~ With insulin it has been found that the crystalsremain unchanged on drying, so that here no precautions arerequired to obtain crystalline diffraction effects.79Only in the case of pepsin and insulin are the data yet sufficientto give some information as to the size and shape of the units present,and these structures appear to be related to one another in a ratherinteresting way. In both cases, approximately spheroidal moleculesof molecular weight about 37,000 appear to be present, but thepacking is very different. In insulin the unit cell is rhombohedral,with a = 44.3, a = 115", and contains a single Svedberg unit ofweight 37,000. The size and shape of this molecule thereforefollow as equivalent to the size and shape of the unit cell, and thepacking together of the molecules is determined exactly by thelattice present. It is actually of a very close 8-co-ordination type.Pepsin, on the other hand, has a rhombohedral cell of dimensionsa = 162 8., a = 23"50', with a cell molecular weight 1,464,000.As this contains about 50% of water, only six Svedberg moleculesof molecular weight about 37,000 are present in the cell.It isimpossible in this case to say exactly how these molecules arearranged or what is their shape; but comparison of the cell dimen-sions and intensities of pepsin with insulin suggests strongly that thepepsin molecules are approximately spherical with radius 20 8. andarranged in a loose 4- co-ordination structure probably related tothat of p-carborundum. Such a structure leaves large channelsbetween the pepsin molecules to be filled with water or with themany impurities from which it is extremely difficult to free theprotein completely.So far this work gives us no information as to what is the actual76 Nature, 1934,133,794; A., 1934, 720; cf. W. T. Astbury and R. Lomax,7 ? R. W. G. Wyckoff and R. B. Corey, Science, 1935,81,365.7 8 J . Amer. Chern. Soc., 1934, 56, 2398.$o (Miss) D. M. Crowfoot, Nature, 1935, 135, 591.bid., p. 795 ; A . , 1934, 720CROWFOOT : MOLECULAR CRYSTALS. 241arrangement of the amino-acid residues inside these globular proteinmolecules, or what is their relation to the fibre proteins, but evidenceof the connexion between the two is coming from several directions.Amongst the fibre proteins, on the one hand, very long spacings havebeen observed for feather keratin by W. T. Astbury and T. C.Marwick,80 for tendon by Wyckoff, Corey, and J. Biscoe,81 and for anumber of materials such as collagen, gelatin, and nerves (thoughthese latter are more probably due to lipins) by G. L. Clark and hisco-workers.82 These long spacings point either to the presenceof large molecules or to the regular repetition a t large intervalsalong the chain of some particular pattern of amino-acid residues.Such a pattern might be produced by the breakdown of somespecial configuration of atoms on the denaturation of a solubleprotein. Astbury has accordingly studied this process in a numberof the plant globulins, and finds that denaturation does in all caseslead to considerable sharpening of the very diffuse rings observed at4.5 and 10A.83 Moreover, denatured fibres of edestin (fromcrystals of which Wyckoff has reported typical long spacings)have all the elastic properties of the fibre proteins and give a well-oriented fibre pattern showing the typical spacings 3.3 8. along thefibre axis and 10 and 4.5 8. across it.s4 Still more illuminatingresults have been obtained on single crystals of excelsin, a plantglobulin of molecular weight 200,000. By keeping this in water,Astbury was able to' obtain a single-crystal pattern showing verylarge spacings, but superimposed on this was a typical fibre patternwhich proved to be definitely oriented with respect to the crystalaxes. After the exposure, the crystal was no longer soluble, althoughin shape and appearance it remained unaltered. An insolublefibrous protein had evidently been obtained by some process ofdegeneration within the crystal. This suggests strongly that,whatever the configuration of the amino-acid residues is within themolecule, it is one that can be converted with very little changeof the mutual positions of the atoms into a fibre form. But whetherwe should imagine the soluble protein as built up of scleroproteinchains, or the scleroproteins as having some other structure relatedin an unknown way to a new and different configuration of residuesin the soluble proteins, remains still to be proved.Nature, 1932, 130, 309. 81 Science, 1935, 82, 175; A., 1266.82 G. L. Clark, E. A. Parker, J. A. Schaad, and W. J. Warren, J . Arner.Chem. Soc., 1935, 57, 1509; A., 1195; F. 0. Schmitt, G. L. Clark, and J. N.Mrgudich, Science, 1934, 80, 567; A., 1935, 231; F. 0. Schmitt, R. S. Bear,and G. L. Clark, ibid., 1935, 82,44; A., 1145.D. M. C.83 W. T. Astbury and R. Lomax, J., 1935, 846.84 W. T. Astbury, S. Dickinson, and K. Bailey, Biochem. J . , 1935,29, 2351 ;A., 1433242 CRYSTALLOQRAPHY,LIQUIDS.It is impossible for reasons of space to include in this section allthe modern developments in the theory of liquids. All that can bedone is to give some references to recent papers on the determinationof the statistical structure of certain liquids by means of X-rays.S. Ka'tzoff S5 has studied water, heptane, decane, benzene, andcyclohexane : in water, a tetrahedral arrangement was found ; 86 inthe others, a statistical close packing of chains or quasisphericalmolecules. B. E. Warren *' has made a Fourier analysis of liquidparaffin and shows that it can be represented by parallel zigzagchains at an average distance of 5.0 A. apart.W. H. Zachariasen88 has shown that in liquid methyl alcoholthere is evidence for hydroxyl bonds. J. A. Prins has studiedthe diffraction of ionic solutions,89 and been able to show that asecondary lattice depending on the concentration exists in some,but not all, ionic solutions.The question of cybotactic groups has been much studied,especially by Stewart and his co-workers.QO Evidence is stillconflicting. These groups almost certainly do exist in long-chainalcohols, but their presence in ethyl ether in the region of the criticalpoint has been disputed by N. S. Gingrich and B. E. Warren,g1who show that the observed diffraction can be explained simplyby a statistical arrangement of a certain mean distance. It isinteresting to note that the diffraction pattern given by liquids inthe neighbourhood of the critical point depends only on the volume,and is practically identical at two temperatures above and belowthe critical temperature when these have the same volume.H. Sirk 92 has shown, by unsuccessful attempts to induce magneticorientation, that the cybotactic group in a hydrocarbon cannotcontain more than 10,000 molecules. J. D. B.J. D. BERNAL.D. M. CROWFOOT.R. C. EVANS.A. F. WELLS.J . Chern. Physics, 1934, 2, 841; A., 1935, 152. Compare H. K. Ward,ibid., p. 153; A., 1934, 587; W. C. Pierce, ibid., 1935,3, 252; J. A. Prins andR. Fonteyne, Physica, 1935,2, 573.8 7 Physical Rev., 1933, [ii], 44, 969; A., 1934, 244.8 8 J . Chern. Physics, 1935, 3, 158.89 Ibid., p. 72; J . A. Prins and R. Fonteyne, Physica, 1935, 2, 570; J. A.Prins, ibid., 1934,1, 1171; A., 1935, 162.9* G. W. Stewart, J . Chern. Physics, 1934,2,147 ; A., 1934, 591 ; C. A. Benzand G. W. Stewart, Physical Rev., 1934, [ii], 46, 703; R. D. Spangler, ibid.,p. 698; ibid., 1932, [ii], 42, 907; A., 1933, 1236.Ibid., 1934, [ii], 48,248; A., 1934, 1160.82 8. Physik, 1934,89.129; A,, 1934, 834.86 See Ann. Reports, 1934, 31, 86